A fuel injection control device controls the calculated fuel injection quantity depending upon the load condition of the engine such that the fuel injection quantity demanded by the engine can be established. This fuel injection quantity is determined based upon engine speed, intake air temperature, engine temperature, the atmospheric pressure of the intake air, and the throttle opening. When the detected intake air temperature is high for a high load condition of the engine, an intake air temperature correction factor is set such that the intake air temperature is less influential upon the establishment of the fuel injection quantity. Moreover, during acceleration, an acceleration incremental fuel injection quantity is calculated based upon different water temperature correction factors. When an engine temperature is low, the fuel injection quantity demanded by the engine is very large. Accordingly, the fuel injection control device utilizes a second water temperature correction factor which is set to be larger than a first water temperature correction factor at low engine temperatures. Thus, the fuel injection quantity for acceleration of the engine at low engine temperatures can be established in accordance with the demand by the engine.