A control device of a lock-up clutch according to the disclosure is mounted on a vehicle including an engine, a transmission, a fluid-type power transmitting device interposed between the engine and the transmission, and the lock-up clutch provided on the fluid-type power transmitting device. The control device includes: a controller configured to slip-engage the lock-up clutch when accelerator opening of the vehicle changes in an accelerating direction, and configured to make a slip-engagement amount larger when a state of the fluid-type power transmitting device when the accelerator opening of the vehicle changes in the accelerating direction is a driven state than the slip-engagement amount when the state of the fluid-type power transmitting device is a driving state.