A fluid pressure control device including a torque converter that is placed between a output shaft of an engine and an input shaft of a transmission, a mechanical oil pump that is driven by the output shaft, a clutch that directly engages the output shaft and the input shaft by employing an engagement pressure based on a fluid pressure that is generated by the mechanical oil pump, an electric oil pump that can supply a fluid pressure to the clutch, and a control unit for controlling the electric oil pump, wherein when the engagement pressure based on the fluid pressure that is generated by the mechanical oil pump is an amount below a necessary engagement pressure that is necessary to engage the clutch, the control unit drives the electric oil pump so as to supply a fluid pressure by at least the amount to the clutch.