To make low the weight and cost of the system of a hybrid electric vehicle, by making constant the shaft output of its engine (rotational speed) generated substitutionally by its generator in the course of its starting.

While the starting of an engine 4 requires a starter, a generator 5 substitutes it. The control of the generator 5 is performed by a converter 10 to control the current of the primary winding of the generator 5. When starting the engine 4, the generator 5 is driven in a power running way. The load of the generator 5 is increased gradually until the rotational speed of the engine 4 reaches the one of it having thereat a good combustion efficiency. The load of the generator 5 is so adjusted by the converter 10 that the rotational speed of the engine 4 does not overshoot the one of it having thereat a good combustion efficiency. Still, when the engine 4 has no load, the rotational speed of its shaft is made higher than the one of it having thereat a good combustion efficiency.