To avoid the risk of taking a long start-up time in the case of automatically stopping an engine in a specified idle stop condition and automatically starting the engine by a motor in a specified idle stop release condition.

When starting by an engine key switch (S2→S10) or when starting after an idle stop (S4→S10), start-up time TZ from the start of start-up until engine speed Ne reaches the specified value, is clocked (S11-S13). The judgment threshold value TO to the start-up time is set according to friction, if necessary (S14), and when the start-up time TZ is the threshold value TO or longer, the subsequent idle stop is inhibited (S15, S17).