A vehicle lock-up clutch control device includes a torque converter, a fuel cutoff control unit and a lock-up release/transmission cooperative control unit. The torque converter is disposed between an engine and a continuously variable transmission. The fuel cutoff control unit is configured to prevent fuel injection to the engine while in a coasting state with the driver's foot away from the accelerator, and configured to restart the fuel injection based on a fuel recovery permission. The lock-up release/transmission cooperative control unit is configured to carry out a cooperative control of a lock-up release control for reducing the clutch engagement capacity of the lock-up clutch and a transmission control for shifting the transmission. Then, if there is an accelerator depression operation while coasting with the lock-up clutch in an engaged state, the lock-up release timing and the shift timing are offset from one another.