This paper proposes a controller to regulate the supply pressure of the hydraulic power unit (HPU) for driving a bipedal robot. We establish flow rate models for charging accumulator, actuating joints and leaking from actuators and spool valves. This determines the pump driving motor speed to satisfy the demanded flow rate for operating the bipedal robot without the energy loss caused by the bypass through a pressure regulating valve. We apply proposed controller to an onboard HPU mounted on top of bipedal robot platform with twelve degrees of freedom. We implement air-walking motion and squat motion which require variable flow rate to the bipedal robot. Through this experiment, the energy efficiency of proposed controller was verified by comparing the electric energy consumed when the controller was applied and when the pump operated at constant speed. We also shows the capability of the HPU’s control performance to regulate supply pressure.