What is claimed is:1. A light-emitting diode (LED) driving circuit, comprising:a) a switching power stage circuit configured to generate a pseudo-constant output current to drive an LED load, wherein said LED load comprises a plurality of LED strings coupled in series between outputs of said switching power stage circuit;b) a loop steady state network comprising a plurality of steady state holding components configured to hold a plurality of steady state control signals that correspond to a plurality of load states of said LED load;c) a switching decoder configured to select one of said plurality of steady state control signals from said loop steady state network based on a plurality of pulse-width modulation (PWM) dimming signals; andd) a control loop configured to generate a first control signal in accordance with a current feedback signal that represents said driving current of said LED load and said selected steady state control signal to control operation of said switching power stage circuit.2. The LED driving circuit of claim 1, wherein said plurality of LED strings are controlled by said plurality of PWM dimming signals to be enabled or disabled from a series LED current path to control average currents flowing through said plurality of LED strings.3. The LED driving circuit of claim 1, wherein said plurality of steady state holding components are configured to hold a state from a prior switching period of said switching power stage circuit.4. The LED driving circuit of claim 1, further comprising a logic circuit coupled to said control loop and configured to generate a gate control signal to control operation of a power switching transistor of said switching power stage circuit in accordance with said first control signal and said plurality of PWM dimming signals.5. The LED driving circuit of claim 4, wherein said logic circuit comprises:a) a NOR-gate configured to generate a second control signal in accordance with said plurality of PWM dimming signals; andb) an AND-gate configured to generate said gate control signal in accordance with said first and second control signals.6. The LED driving circuit of claim 1, wherein:a) said control loop is configured to be operated at a peak current control mode with a constant frequency; andb) a compensation signal of said control loop is determined by said plurality of steady state control signals.7. The LED driving circuit of claim 6, wherein said control loop comprises:a) a transconductance amplifier configured to generate a current error signal in accordance with said current feedback signal and a reference voltage, wherein said loop steady state network is configured to generate a compensation signal in accordance with said current error signal;b) a first comparator configured to generate a first comparison signal in accordance with said compensation signal and said current feedback signal; andc) an RS flip-flop having a reset terminal coupled to said first comparison signal, a set terminal coupled to a clock signal, and an output terminal configured to generate said first control signal.8. The LED driving circuit of claim 7, wherein said plurality of steady state holding components comprises:a) a plurality of compensation capacitors coupled in parallel; andb) a plurality of switching circuits, wherein each switching circuit is coupled in series with a corresponding of said plurality of compensation capacitors to control selection thereof.9. The LED driving circuit of claim 8, wherein said plurality of compensation capacitors are configured to hold voltage values of said compensation signal.10. The LED driving circuit of claim 1, wherein said control loop is configured to be operated in a constant off time control mode, and wherein an off time of said control loop is determined by said steady state control signals.11. The LED driving circuit of claim 10, wherein said control loop comprises:a) a transconductance amplifier configured to generate a current error signal in accordance with said current feedback signal and a reference voltage;b) an error compensation circuit configured to generate a compensation signal in accordance with said current error signal;c) a first comparator configured to generate a first comparison signal in accordance with said compensation signal and said current feedback signal;d) a constant time generation circuit configured to generate a second comparison signal in accordance with said control signal to control an off time of said power switching transistor to be substantially constant, wherein said off time is determined by said plurality of steady state control signals; ande) an RS flip-flop having a reset terminal coupled to said first comparison signal, a set terminal coupled to said second comparison signal, and an output terminal configured to generate said first control signal.12. The LED driving circuit of claim 11, wherein said constant time generation circuit comprises:a) a slope signal generation circuit configured to generate a slope signal in accordance with said first control signal;b) a reference voltage generation circuit configured to generate a reference voltage signal; andc) a second comparator configured to generate said second comparison signal in accordance with said slope signal and said reference voltage signal.13. The LED driving circuit of claim 12, wherein said plurality of steady state holding components comprises:a) a plurality of voltage sources; andb) a plurality of switching circuits, wherein each switching circuit is coupled in series with a corresponding of said plurality of voltage sources to control selection thereof, and wherein said selected of said plurality of voltage sources is configured as said reference voltage signal.14. The LED driving circuit of claim 12, wherein said steady state holding components comprises:a) a plurality of filtering circuits; andb) a plurality of switching circuits, wherein each switching circuit is coupled in series with a corresponding of said plurality of filtering circuits to control selection thereof, and wherein said selected of said plurality of filtering circuits is configured to generate said reference voltage signal.15. The LED driving circuit of claim 11, wherein said power switching transistor is configured to be turned off and said transconductance amplifier is disconnected from said control loop when all of said plurality of LED strings are turned off.16. The LED driving circuit of claim 11, wherein a number of said plurality of LED strings M is related to a number of said steady state holding components N by N=2M.17. A driving method for a light-emitting diode (LED) load, the method comprising:a) generating, by a control loop, a first control signal in accordance with a current feedback signal representing a driving current flowing through an LED load, wherein said LED load comprises a plurality of LED strings coupled in series coupled between outputs of a switching power stage circuit;b) holding, by a plurality of steady state holding components in a loop steady state network, a plurality of steady state control signals corresponding to a plurality of load states of said LED load;c) selecting, by a switching decoder, one of said plurality of steady state holding components from said loop steady state network based on a plurality of pulse-width modulation (PWM) dimming signals, for generating said first control signal when a state of said LED load varies; andd) generating, by said switching power stage circuit, a pseudo-constant output current to drive said LED load.18. The method of claim 17, further comprising controlling, by said plurality of PWM dimming signals, average currents flowing through said plurality of LED strings that a different luminance can occur for each said LED string.19. The method of claim 18, further comprising:a) operating said control loop at a peak current control mode with a constant frequency; andb) determining a compensation signal of said control loop by said plurality of steady state control signals.20. The method of claim 18, further comprising:a) operating said control loop in a constant off time control mode; andb) determining an off time of said control loop by said steady state control signals.21. The LED driving circuit of claim 2, further comprising a plurality of switches, wherein each of said plurality of switches is coupled in parallel with a corresponding one of said plurality of LED strings, and wherein said plurality of switches are controlled by said plurality of PWM dimming signals.22. The LED driving circuit of claim 1, wherein said switching power stage circuit comprises a power switching transistor and an inductor, wherein said power switching transistor is configured to be turned off to discharge said inductor.23. A light-emitting diode (LED) driving circuit, comprising:a) a switching power stage circuit comprising a power switching transistor and an inductor, wherein said switching power stage circuit is configured to generate an output current to drive an LED load having a plurality of LED strings;b) a controlling circuit configured to receive a plurality of pulse-width modulation (PWM) dimming signals corresponding to said plurality of LED strings, to control an average current flowing through said plurality of LED strings using said plurality of PWM dimming signals, and to regulate a current reference signal in accordance with a PWM control signals;c) a current control circuit configured to control said output current in accordance with said current reference signal and a current feedback signal that represents said output current, in order to satisfy a driving current of said plurality of LED strings;d) a loop steady state network comprising a plurality of steady state holding components configured to hold a plurality of steady state control signals that correspond to a plurality of load states of said LED load;e) a switching decoder configured to select one of said plurality of steady state control signals from said loop steady state network based on said plurality of PWM dimming signals; andf) a control loop configured to generate a first control signal in accordance with a current feedback signal that represents said driving current of said LED load and said selected steady state control signal to control operation of said switching power stage circuit.24. The LED driving circuit of claim 23, further comprising a plurality of switching circuits corresponding to said plurality of LED strings, wherein each said switching circuit is controlled by a corresponding PWM dimming signal in order to turn on or off one corresponding LED string.25. The LED driving circuit of claim 24, wherein each of said plurality of switching circuits comprises a controllable switch that is controlled by a corresponding PWM dimming signal.26. The LED driving circuit of claim 25, wherein said controllable switch is coupled in parallel with said corresponding LED string.