A controller has a command section, a control section, a time measurement section, and a command fixing section. The command section generates a command regarding the actuation state of a lock-up clutch in accordance with a condition value that is determined by the accelerator operating amount and the vehicle speed. The time measurement section starts to measure time when the accelerator operating amount drops to 0 with the current condition value maintained in a hysteresis range and the command section generates the acceleration slip executing command. When the accelerator operating amount is increased from 0, the time measurement section stops the measurement of time and resets the measured time to 0. The command fixing section fixes the command of the command section as an acceleration slip executing command in the period from when the time measurement by the time measurement section has started to when the measured time reaches a determination value. When the accelerator operating amount is increased from 0 or the time measured by the time measurement section reaches the determination value, the command fixing section cancels the fixation of the acceleration slip executing command.