A predetermined control on an engine, i.e., a fuel-cut operation, is executed after an accelerator has been released under predetermined conditions when vehicle speed is higher than a fuel-cut vehicle speed value and engine speed is higher than or equal to a fuel-cut engine speed value. In an automatic transmission drivingly connected to the engine via a torque converter, a gear shift is initiated after the accelerator has been released. During a shift of the same kind, there occurs a variability in shift shock between the cases with and without the execution of the fuel-cut operation. In order to reduce this variability, the execution of the fuel-cut operation is inhibited until completion of the shift after the accelerator has been released under the predetermined conditions.