A hysteresis control method for inverter and an inverter based on hysteresis control are disclosed. The inverter is electrically connected to a power grid, and the method includes: Step S1, sampling a grid voltage Vg(z) and an output current Ig(z) of the inverter; Step S2, calculating a present period hysteresis bandwidth H(z) based on the grid voltage Vg(z) sampled in step S1; Step S3, predicting a next period hysteresis bandwidth H(z+1); Step S4, correcting the present period hysteresis bandwidth H(z) based on the next period hysteresis bandwidth H(z+1) obtained in step S3, to obtain a final hysteresis bandwidth Hout(z); and Step S5, controlling an output driving signal according to the output current Ig(z) of the inverter and the final hysteresis bandwidth Hout(z) to control the operation of the inverter.