A torque converter lockup capacity control device is configured to conduct coast-time lockup control during coast-running in order to prevent engine stall, shock from occurring in the output shaft of a transmission due to lockup when a driver releases an acceleration pedal and the running condition switches from a drive running condition to a coast-running condition. Torque converter lockup occurs because the engine output torque drops from a time on when the throttle opening degree becomes zero. Thus, during a period from the time on until fuel cut-in at time, the lockup capacity is lowered to a minimum capacity corresponding to a standby pressure and lockup is avoided. The lockup capacity is raised to a larger value from the predetermined time on, and ordinary coast-time lockup control is executed.