The disclosure relates to a control circuit and a control method for a power converter. The power converter comprises a power switch and an inductor being coupled to the power switch. The control circuit controls operation of the power switch to charge and discharge the inductor for generating an inductor current and providing an output current. The control circuit controls the power switch to be turned on when or after an inductor current detection signal is zero, and controls the power switch to be turned off when the inductor current detection signal reaches a peak reference signal or when the power switch has been turned on for a maximum on time. The control circuit also adjusts the maximum on time in accordance with the inductor current detection signal, so that the power converter provides a constant output current to a load. The control circuit operates at a peak-value current mode and maintains the current of the power converter nearly stable without obtaining a compensation signal. The circuit structure is simplified and the number of peripheral components is reduced.