A carburetor for an internal combustion engine with an accelerator fuel pump in the carburetor having a piston actuated by a cam on a throttle valve shaft and a ball between them. The axis of a pump chamber in which the piston is slidably received is offset from and eccentric to the axis of rotation of the throttle shaft so that little fuel is supplied to the operating engine by the accelerator pump as the shaft is rotated to move the throttle valve from its idle position to an intermediate position and most of the fuel supplied by the accelerator pump to the engine is delivered as the shaft is rotated to move the throttle valve from the intermediate position to its wide open throttle position. This provides a proper fuel mixture to the engine to accelerate it and avoids the problem of supplying an overly rich fuel mixture to the engine during acceleration and particularly if the operator moves the throttle valve several times back and forth between the idle and intermediate positions before moving the throttle valve to the wide open position to accelerate the engine.