An engine automatic speed control apparatus which exhibits a smooth transition from brake release to an engine drive state. An ECU determines braking force such that a vehicle does not move in correspondence with the slope of a road surface according to a road surface slope sensor while monitoring an operated quantity of a brake pedal according to a brake pedal operated-quantity sensor. The ECU stops an engine when braking force is applied via the brake pedal such that the vehicle does not move. After stopping the engine, the ECU determines braking force such that the vehicle does not move in correspondence with slope of the road surface according to the road surface slope sensor, and restarts the engine when braking force becomes less than braking force required to maintain the vehicle in a stopped state. The ECU then restarts the engine in the interval from relaxing of braking force via the brake pedal until the brake pedal is released.