An engine rotational speed control apparatus is provide to prevent a degradation of fuel efficiency caused by an unnecessary increase of the rotational speed of an engine when a depression amount of an accelerator pedal is briefly increased and then immediately decreased. In particular, when the vehicle is accelerated, an optimum fuel efficiency operating point along an optimum fuel efficiency curve is not moved immediately to another optimum fuel efficiency operating point corresponding to a new target drive force. Instead, the target drive force is reached by increasing the engine load while increasing the engine rotational speed as little as possible, and thus using an operating point that does not lie on the optimum fuel efficiency curve.