In an electromagnetically controlled inlet valve actuator provided to a high pressure fuel pump, an impinging sound which is generated at the time of operating the mechanism is reduced. In a high pressure fuel pump provided with an electromagnetically controlled inlet valve (operated by way of a plunger rod), a current supply period includes a 1st current supply period for performing an operation of attracting the plunger rod in a valve closing direction, a 2nd current supply period for alleviating a speed at which the plunger rod moves in a valve opening direction, and a limited current supply period disposed between the 1st current supply period and the 2nd current supply period in the form of spanning a pump top dead center.