A switch-mode power supply and associated control circuit for a light-emitting device are disclosed. The switch-mode power supply having a first switch which is turned ON or OFF by a control signal. The control circuit having an error amplifier, a minimum-off time control circuit and a logic circuit, wherein the error amplifier is configured to provide a compensation signal based on a dimming signal and a feedback signal. The minimum-off time control circuit is configured to provide a minimum-off time control signal to adjust a minimum-off time period of the first switch based on the compensation signal. The logic circuit is configured to provide the control signal based on the minimum-off time control signal.