Lock-up control for torque converter

A lock-up control system including a lock-up differential pressure generator and a controller that is programmed to: when increasing a lock-up differential pressure command value with time to establish the lock-up state of the torque converter, switch a gradient of the lock-up differential pressure command value from a first gradient to a predetermined gradient larger than the first gradient when an actual slip rotation speed is decreased to a predetermined slip rotation speed value or less; and switch the gradient of the lock-up differential pressure command value from the predetermined gradient to a second gradient smaller than the predetermined gradient when the actual slip rotation speed exceeds the predetermined slip rotation speed value again after being decreased to the predetermined slip rotation speed value or less.