PURPOSE: To prevent exhastion of a battery used in a vehicle in which an elec tric auxiliary driving system for an internal combustion engine is mounted.

CONSTITUTION: An electric auxiliary driving system for an internal combustion engine is provided in a such a constitution that auxiliary torque is given from an electric machine (an alternating current rotator 3) to an internal combustion engine (a diesel engine 1) at the time of starting and accelerating of a vehicle. In this system, charging condition of a battery 8 is detected by a battery condition detector 14 so as to find out the charging rate α of the battery 8 (step S103). An auxiliary torque amount able to be supplied from the alternating current rotator 3 to the diesel engine 1 is calculated on the basis of the charging rate α (step S104). A fuel amount given to the diesel engine 1 and a load ratio of the alternating current rotator 3 are changed by the auxiliary torque amount capable of being supplied (step S105 to S108). It is thus possible to prevent exhaustion of the battery 8 when the charging rate α becomes in a low level, without using the alternating current rotator 3 as the electric machine even if the auxiliary torque is necessitated.