The invention relates to a fluid conveyance system for a fluid, comprising a low-pressure conveyance system having a low-pressure pump (2) and a high-pressure conveyance system having a high-pressure pump (8), which are connected by means of a connecting line, wherein the fluid conveyance system has a pressure damper (19). According to the invention, a fluid conveyance system is provided, by means of which a pulsation of the fluid caused by flow-rate waves or pressure waves in the fluid is damped. This is achieved in that the pressure damper (19) is arranged in the lower-pressure conveyance system and is a hydraulic pressure damper (19). Said hydraulic damper (19) has a piston (21) arranged in a cylinder (20), which piston can be moved against the force of a compression spring (23) and the vapor pressure present in a compression-spring chamber (22) accommodating the compression spring.