The direct voltage feed-forward control is used in converter control to suppressing the grid voltage distortion. But the delay in the system makes the feed-forward voltage be out of the phase with the actual grid voltage. So the effect of suppressing the voltage distortion is seriously affected. In order to decrease the influence of the delay on the direct voltage feed-forward control, and improve the suppression ability of voltage distortion, the feed-forward control based on grid voltage prediction is proposed aiming at the periodic voltage distortion. The actual grid voltage magnitude at the PWM loading moment is forecasted by using the sampled grid voltage magnitude in previous power frequency periodic, and the better synchronization between the feed-forward voltage and the actual grid voltage is guaranteed. The simulation and experimental results verify that the inhibition rates at frequencies of 3rd,5th,7th,and 11th voltage harmonics are improved from 94%,84%,72%,42% to 99%,97%,94%,85%,by the feed-forward control based on grid voltage prediction, and the output current of the converter can be improved when the grid voltage is distorted.