A power converter for an LED drive circuit, can include: a capacitor and an LED load coupled in parallel to receive an output signal of a rectifier circuit; a power switch coupled in series with the LED load, and being configured to control a current path from the rectifier circuit to the LED load; and a control circuit configured to control the power switch to be turned off in accordance with an error between an output current flowing through the LED load and a desired current value to decrease power consumption of the power switch, where the operation of the power switch is controlled to transition between on and off states in each sinusoidal half-wave period.