To secure the 'engine brake' performance and improve fuel consumption by turning on the lock-up clutch of an A/T vehicle, and reducing idle engine speed at a fixed vehicle speed or above.

Whether the vehicle speed detected by a vehicle speed sensor exceeds a fixed vehicle speed B Km/h or not is judged (S1). If the vehicle speed is B Km/h or above, whether an idle switch is turned on or not is judged (S2). If the idle switch is turned off, a lock-up clutch is turned off (S5). If the idle switch is turned on, the lock-up clutch is turned on by a lock-up clutch solenoid (S3), the idle engine speed is set to a constant engine speed Crpm against the water temperature (S4). If the vehicle speed is BKm/h or below, whether the vehicle speed is 0Km/h or not is judged (S6). If the judgement is yes, whether the engine water temperature is below A°C or not is judged (S7). If the engine water temperature is below A°C, the idle engine speed is increased. If the engine water temperature is A°C or above, the idle engine speed is set to the constant engine speed Crpm (S4).