A fuel supply system for an engine having no fuel return pipe is disclosed. In steps target fuel is set according to an engine operating state. Thereafter, a target current value to be supplied to the motor of a fuel pump according to the target fuel pressure is obtained. In the succeeding step, an actual motor current is detected and, then, the target current value and the detcted current are compared. Thereafter, the supply current is controlled by feedback based upon the difference obtained by comparison between the target current value and the detected current value to eliminate the difference.