According to a discrete repetition sliding mode control method for an inverter, a difference between preset inverter voltage and actual inverter voltage is used as a repetition sliding mode controller error; the preset inverter voltage is as an input of a feedforward transfer function and an index double-power approach rate; a summation of a repeated controlled output and a repeated sliding mode controller error is used as the input of the sliding mode controller on the condition of equivalent control; and a summation of the output of the feedfoward transfer function, the output of the sliding mode controller and the output of the index double-power approach rate is used as a control signal for switching on or switching off an inverter bridge switch tube in an inversion step. According to the discrete repetition sliding mode control mode, repeated control and sliding mode control are combined based on an equivalent control method in a discrete domain, thereby realizing advantages of high state precision in repeated control and high dynamic speed and high robustness in sliding mode control. Furthermore the index double-power approach rate can improve system dynamic response speed. According to the discrete repetition sliding mode control method, designing is performed in the discrete domain, and a result more accords with an actual system.