An engine control apparatus predicts the speed of an engine in a normal rotation range as a function of a loss energy in an engine rotation pulsating period and also predicts the speed of the engine in a reverse rotation range as a function of a pumping loss component and a loss energy which is derived by reversing the sign of a value of a friction component that is a portion of the loss energy in the normal rotation range and arises from mechanical friction to which the piston is subjected during stroke thereof. The pumping loss component is an energy loss occurring in the intake stroke of the engine. This calculation enhances the accuracy in predicting a future engine speed between start of a drop in speed of the engine resulting from stop of combustion of fuel and stop of rotation of the engine.