The invention provides a high-pressure fuel supply pump. A damper mechanism used for a high-pressure fuel supply pump system has a problem in that its total height is high and its external diameter is also large. In cases where the damper mechanism is integrally attached to the high-pressure fuel supply pump, the total height of the high-pressure fuel supply pump becomes high and the external diameter of the pump also becomes large. The damper mechanism of the present invention is configured so that an outer circumferential surface of a cover in regard to the thickness direction of the base material of the cover engages with the inner circumference of an open end part of a bottomed tubular concave part formed in a damper housing or in a pump housing of the high-pressure fuel supply pump. With this configuration, the total height of the damper as a low-pressure pulsation reducing mechanism can be reduced and the dimensions of the damper in the radial directions can also be reduced. In cases where the damper mechanism is formed integrally with the high-pressure fuel supply pump, the total height of the high-pressure fuel supply pump can be reduced, the dimensions of the damper part in the radial directions can also be reduced, and a high-pressure fuel supply pump in a small body size can be provided.