Motor control apparatus for an electric oil pump includes the control command generating section configured to drive the motor control section by the first current command signal obtained from the fixed second target torque signal of the second signal generating section in a first stage, when the control command generating section receives the start command of the motor from the host control device when engine stops, to output the sum signal of the first current command signal and the second current command signal to the current control section, and to drive the motor control section by the third current command signal in a second stage, and to switch the output of the target torque switching section from the fixed second target torque signal to the first target torque signal of the first signal generating section in a third stage.