A simple and compact fuel supply system which prevents generation of fuel vapor in a delivery pipe of an engine includes a check valve is disposed at a down stream portion of a fuel pressure relieving member or a fuel pressure regulator to seal the fuel delivery pipe when the engine stops so that the pressure in the delivery pipe increases as fuel vapor is generated and, consequently, generation of the fuel vapor is automatically suppressed. Transmission of a pressure wave from the delivery pipe caused while injectors are operating is prevented by the check valve so that harsh noise, which is otherwise caused by resonant vibration of fuel supply pipes and related members, is suppressed.