The fuel supply system of an internal combustion engine includes an electronic control unit (ECU) for transferring the engine from a state in which a high-pressure fuel pump does not deliver any pressurized fuel to a state in which the high-pressure fuel pump begins to deliver the pressurized fuel by gradually varying an output period of a drive signal for controlling opening/closing behavior of a solenoid valve while monitoring changes in fuel pressure detected by a pressure sensor, and for estimating a mounting error between angular mounting positions of the high-pressure fuel pump and a pump actuating cam with reference to a rotation signal from a state of the solenoid valve drive signal when a change in the fuel pressure has been detected. The solenoid valve drive signal is corrected based on the value of the mounting error estimated by the ECU.