A controller includes a control unit which is configured to execute a coast stop control. The coast stop control is configured to perform automatic stopping of the drive source while the vehicle is traveling, when a permitting condition is satisfied, the permitting condition including a condition that a speed ratio R of the variator is lower than a first threshold R1 while the lock-up clutch is in an engaged phase. The control unit is configured to prohibit execution of the coast stop control in a case in which an input-output rotation speed difference of the torque converter is equal to or more than a predetermined value when the lock-up clutch is in the engaged phase.