A variable delivery type fuel supply apparatus capable of suppressing variation of fuel pressure within a delivery pipe and hence variation of fuel quantity injected through fuel injection valves and simplifying a control method therefor. The apparatus includes an oil relief passage (6) provided between the suction port of a fuel pump (4) and a pressurizing chamber (4e) across a suction valve (4a) of the fuel pump (4), an electromagnetic valve (7) disposed in the oil relief passage (6) and opened for a predetermined time during a discharge stroke of the fuel pump (4) for thereby controlling a discharge quantity of the fuel pump (4), and a control unit (108) for controlling the timing at which the electromagnetic valve (7) is opened. The control unit (108) is so designed as to control open/close operations of the electromagnetic valve (7) such that a time point for starting electrical energization of the electromagnetic valve (7) is fixedly set at a predetermined time point relative to the suction/discharge stroke of the fuel pump (4) while allowing the time point for terminating the electrical energization to be variable, to thereby control the discharge quantity of the fuel pump (4).