To provide an acceleration pump mechanism included in a fuel supply system of an engine which secures excellent engine restartability by preventing fuel from leaking out into an intake passage through an acceleration nozzle from engine stop until the time immediately before restart.

An acceleration pump mechanism 1A includes an acceleration fuel chamber 20a for introducing fuel for acceleration from a constant fuel chamber 3 to be stored therein, a fuel pressurization means for pressurizing fuel in the acceleration fuel chamber 20a in synchronization with engine acceleration operation, and an acceleration fuel passage 29 for feeding pressurized fuel to an acceleration nozzle 23 of an intake passage 4, and additionally supplies fuel for acceleration at engine acceleration, wherein a cutoff valve 130 for blocking the circulation of fuel by being closed at engine stop is provided to the acceleration fuel passage 29. At least from engine stop until the time immediately before restart, fuel is prevented from leaking out into the intake passage 4 through the acceleration nozzle 23.