A hydraulic pressure supply system, which is capable of properly controlling a degree of engagement of a clutch, thereby making it possible to improve vehicle drivability. The hydraulic pressure supply system includes a first hydraulic pressure supply device that uses an internal combustion engine as a motive power source and supplies hydraulic pressure to the clutch, and a second hydraulic pressure supply device that supplies hydraulic pressure to the clutch by being driven by a motive power source other than the engine, detects a vehicle speed and a rotational difference parameter that represents a difference in rotational speed between an output shaft of the clutch and an input shaft of the clutch, and controls clutch supply hydraulic pressure which is hydraulic pressure supplied to the clutch, according to the detected vehicle speed and rotational difference parameter, when restart conditions of the engine are satisfied.