A high-pressure fuel supply pump having an electromagnetically driven intake valve, comprising: a pump housing in which a pressurizing chamber is provided; a piston plunger supported by the pump housing, the piston plunger repetitively performs a reciprocating motion within the pressurizing chamber to suck fluid into the pressurizing chamber, pressurize the fluid therein and discharge the fluid out of the pressurizing chamber; an electromagnetically driven intake valve unit attached to the pump housing; the electromagnetically driven intake valve unit including an intake valve device provided at an inlet of the pressurizing chamber and an electromagnetic driving mechanism for controlling an opening or closing timing for the intake valve device; and the intake valve device including a valve provided on the side of the pressurizing chamber, a valve seat and a valve stopper provided in a valve housing; wherein the valve includes an annular abutting surface that abuts the valve seat to shut off a fuel intake passage and a bottomed cylindrical part provided at an inner peripheral part of the annular abutting surface; a valve biasing spring is provided for biasing the valve to the valve seat, and characterized in that the bottomed cylindrical part is constituted by a bottom flat surface and a cylindrical part, which passes through an opening part formed at the valve housing radially inside the valve seat, with the outer surface of an end part of the bottomed cylindrical part protruding in a low pressure fuel chamber provided upstream of the opening part. a pump housing in which a pressurizing chamber is provided; a piston plunger supported by the pump housing, the piston plunger repetitively performs a reciprocating motion within the pressurizing chamber to suck fluid into the pressurizing chamber, pressurize the fluid therein and discharge the fluid out of the pressurizing chamber; an electromagnetically driven intake valve unit attached to the pump housing; the electromagnetically driven intake valve unit including an intake valve device provided at an inlet of the pressurizing chamber and an electromagnetic driving mechanism for controlling an opening or closing timing for the intake valve device; and the intake valve device including a valve provided on the side of the pressurizing chamber, a valve seat and a valve stopper provided in a valve housing; wherein the valve includes an annular abutting surface that abuts the valve seat to shut off a fuel intake passage and a bottomed cylindrical part provided at an inner peripheral part of the annular abutting surface; a valve biasing spring is provided for biasing the valve to the valve seat, and characterized in that the bottomed cylindrical part is constituted by a bottom flat surface and a cylindrical part, which passes through an opening part formed at the valve housing radially inside the valve seat, with the outer surface of an end part of the bottomed cylindrical part protruding in a low pressure fuel chamber provided upstream of the opening part. a valve biasing spring is provided for biasing the valve to the valve seat, and characterized in that the bottomed cylindrical part is constituted by a bottom flat surface and a cylindrical part, which passes through an opening part formed at the valve housing radially inside the valve seat, with the outer surface of an end part of the bottomed cylindrical part protruding in a low pressure fuel chamber provided upstream of the opening part.