An output power of the internal combustion engine (1) is transmitted to a drive wheel via a torque converter (2B) having a pump impeller and a turbine runner. A lockup clutch (2C) directly connects the pump impeller and the turbine runner during a coast running of a vehicle. When the accelerator pedal is slightly depressed during a coast running of a vehicle in a fuel cut-off state, the lockup clutch (2C) disengages. In addition, fuel recovery of the internal combustion engine (1) is suppressed until the engaging pressure of the lockup clutch (2C) decreases, thereby preventing a vehicle speed change caused by an output power increase of the internal combustion engine (1) before the lockup clutch (2C) substantially disengages.