An unlock operation of a lockup clutch and a shift-up operation of an automatic transmission are performed together when an accelerator pedal of a vehicle is released in a state where the lockup clutch is in a lockup state. An engine rotation speed immediately after the shift-up operation is estimated on the basis of the engine rotation speed and a gear ratio of the automatic transmission after the shift-up operation. If a fuel recovery operation is predicted to be performed immediately after the shift-up operation, the fuel-cut operation is prevented, thereby suppressing a shock from occurring due to the fuel recovery when a foot release shift-up operation is performed.