A lock-up controller of a lock-up control system reads-in a vehicle speed V, a throttle opening degree TVO, an engine speed Ne, and a turbine speed Kt from sensors and outputs a fuel-out command and a fuel-supply restart command to an engine controller, to operate a lock-up clutch in a torque converter of an automatic transmission for an automotive vehicle in an accelerator-off (coasting) state of the vehicle. The lock-up control system makes it possible to realize locking-up of the torque converter providing an improved fuel consumption ratio of the engine and a large braking force from the engine, even when a vehicle speed increases due to running down a downward slope while the accelerator-off state continues, or when an up-shifting speed change occurs due to the accelerator-off state.