A control method of a high pressure fuel pump provided with an electromagnetically controlled inlet valve wherein the high pressure fuel pump comprises: an inlet passage for introducing fuel into a pressurizing chamber ; an outlet passage for discharging the fuel from the pressurizing chamber ; a pressurizing member which reciprocates in the pressurizing chamber ; an inlet valve provided between the inlet passage and the pressurizing chamber ; a first spring (S4) biasing the inlet valve in the valve closing direction; an outlet valve provided between the outlet passage and the pressurizing chamber ; and an electromagnetic actuator for controlling an operation of the inlet valve, wherein the electromagnetic actuator comprises: a second spring , a plunger rod biased by the second spring ; and an electromagnetic solenoid device which generates an electromagnetic force in the direction opposite to a biasing force of the second spring corresponding to an electric current which flows in a solenoid , and is configured to control an operation of the inlet valve such that, by balancing a biasing force of the second spring and the electromagnetic force, the plunger rod is moved to a first position or a second position thus making the plunger rod engaged with the inlet valve or releasing the engagement between the plunger rod and the inlet valve, and a current supply period includes: a 1st current supply period during which an electromagnetic force which is stronger than the biasing force of the second spring and moves the plunger rod to the first position from the second position is generated; a 2nd current supply period during which energy which moves the plunger rod to the second position is reduced by giving a force weaker than a force in the 1st current supply period, and a limited current supply period which is provided between the 1st and the 2nd current supply periods and during which a limited electric current which is set smaller than a peak current in the 1st current supply period (including zero) is supplied in a period during which the inlet valve is closed; wherein at a timing where the pressurizing member of the pump almost reaches a top dead center, the electromagnetic actuator is controlled to the limited current supply period. the electromagnetic actuator comprises: a second spring , a plunger rod biased by the second spring ; and an electromagnetic solenoid device which generates an electromagnetic force in the direction opposite to a biasing force of the second spring corresponding to an electric current which flows in a solenoid , and is configured to control an operation of the inlet valve such that, by balancing a biasing force of the second spring and the electromagnetic force, the plunger rod is moved to a first position or a second position thus making the plunger rod engaged with the inlet valve or releasing the engagement between the plunger rod and the inlet valve, and a current supply period includes: a 1st current supply period during which an electromagnetic force which is stronger than the biasing force of the second spring and moves the plunger rod to the first position from the second position is generated; a 2nd current supply period during which energy which moves the plunger rod to the second position is reduced by giving a force weaker than a force in the 1st current supply period, and a limited current supply period which is provided between the 1st and the 2nd current supply periods and during which a limited electric current which is set smaller than a peak current in the 1st current supply period (including zero) is supplied in a period during which the inlet valve is closed; wherein at a timing where the pressurizing member of the pump almost reaches a top dead center, the electromagnetic actuator is controlled to the limited current supply period. <EOS>