The present invention discloses CVCC circuits and methods with improved load regulation for an SMPS. In one embodiment, the CVCC can include: a voltage feedback circuit to generate an output voltage feedback signal; a current feedback circuit to generate an output current feedback signal; a control signal generating circuit that receives the output voltage feedback signal and the output current feedback signal, and generates a constant voltage/constant current control signal; a first enable signal generating circuit that compares a first reference voltage and the constant voltage/constant current control signal to generate a first enable signal; and a PWM controller that generates a PWM control signal based on the constant voltage/constant current control signal to control a main switch of the flyback SMPS.