As a vehicle runs, current load q(t) is calculated every given time. The current load q(t) can be calculated by multiplying the amount of air taken into an engine of the vehicle by the engine speed. Added-up load Q(t) can be found by adding up the current load q(t) according to expression of Q(t)=Q(t-1)+((q(t)-Q(t-1))/a). If the added-up load Q(t) exceeds an inhibition determination value Z, idling stop is inhibited, so that overheating of the engine can be prevented appropriately.