At vehicle stop judgment time t1, a first engine automatic-stop control permission judgment, based on idle stop permission conditions by which an instant permission judgment can be possible, is carried out. If a result of the first engine automatic-stop control permission judgment at time t1 is “permitted”, the second engine automatic-stop control permission judgment, based on an idle stop permission condition which requires a certain time for the judgment, is initiated, and an electric oil pump ON (drive) command (the test drive command) is issued. At time t2 at which an actual drive of the electric oil pump in response to the test drive command is detected, it is judged that a failure of an electric system of the electric oil pump and a foreign matter-biting failure of the electric oil pump do not occur, then a failure judgment of the electric oil pump becomes “normal”. This judgment is completed before time t3 at which the second engine automatic-stop control permission judgment ends, and both of “permitted” of a result of the second engine automatic-stop control permission judgment and “normal” of the failure judgment of the electric oil pump, an idle stop ON command is not outputted.