A vehicle control device has an engine, automatic transmission, and torque converter disposed between the engine and the automatic transmission. The torque converter includes a lockup clutch coupling an input member to an output member of the torque converter. The control device has: a slip control portion controlling lockup clutch slip when deceleration running; and a fuel cut control portion performing an engine fuel cut when deceleration running and to terminate the fuel cut when an engine rotation speed is reduced to a predetermined rotation speed or less during the fuel cut, the fuel cut control portion being permitted to perform the fuel cut, based on lockup clutch slip pressure controlled by the slip control portion has reached a slip pressure value at which the engine rotation speed does not decrease due to a shortage of torque capacity of the lockup clutch even when the fuel cut is performed.