An internal combustion engine (2) of a vehicle (1A, 1B) is automatically stopped when a first automatic stopping condition is established while the vehicle is stationary or a second automatic stopping condition is established while the vehicle travels. The first automatic stopping condition requires a road gradient equal to or smaller than a first gradient threshold, and the second automatic stopping condition requires the road gradient equal to or smaller than a second gradient threshold. By setting the second gradient threshold at a smaller value than the first gradient threshold, a feeling of unease experienced by a driver when the engine is stopped on a slope is reduced.