To obtain a small and high performance damper mechanism which reduces pressure pulsation in low pressure-side fuel in the high pressure fuel pump in a high pressure fuel supply system or a high pressure fuel pump provided with the small and high performance damper mechanism. Two metal diaphragms are welded together over the entire circumference to obtain a metal diaphragm assembly (also referred to as “double metal diaphragm damper”). The whole or part of the portion of the metal diaphragm assembly other than the weld (for example, the portion inside the weld) is clamped by a pressing member and thereby the assembly is secured in a housing enclosure. The housing enclosure may be formed integrally with the body of a high pressure pump.