A pump apparatus including a pump housing, a drive shaft, a cam ring movably disposed in the pump housing, a pump element disposed within the cam ring and rotationally driven by the drive shaft to vary a specific discharge quantity which is a discharge quantity of the working oil per one rotation of the pump element in accordance with variation in eccentric amount of the cam ring with respect to the drive shaft, and a solenoid which is drivingly controlled on the basis of a steering condition and a vehicle speed and operated to control the eccentric amount of the cam ring. The solenoid is controlled to execute a flow rate reduction control during cranking of an engine of the vehicle in which the cam ring is allowed to move in such a direction as to reduce the specific discharge quantity.