The damper mechanism used for a high-pressure fuel supply pump 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. 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 and the dimensions of the damper part in the radial directions can also be reduced.