In a fuel supply apparatus for an internal combustion engine, asynchronous fuel supply or injection is effected in addition to synchronous fuel injection so as to increase fuel amount on acceleration. In order to reduce time lag for supplying additional fuel, the opening degree and opening speed of a throttle valve of the engine are detected, and additional fuel supply by way of asynchronous fuel injection is effected whenever it is determined that the state of the throttle valve represents a state where fuel increase is required. Asynchronous fuel supply is then stopped when the opening degree of the throttle valve reaches an upper limit determined by the detected opening speed of the throttle valve, thereby avoiding application of excessively rich mixture.