A control device of a lock-up clutch provided between an engine and an automatic transmission mechanism mounted in a vehicle by hydraulic pressure, the control device comprising: a coasting judgment unit configured to judge whether the vehicle is in a coasting travel state; an acceleration judgment unit configured to judge depression of an accelerator pedal of the vehicle, return of the depression of the accelerator pedal, acceleration ON and acceleration OFF; and a control unit configured to control a torque transmission capacity (C LU) of the lock-up clutch on the basis of judgment information of the coasting judgment unit and the acceleration judgment unit, and the control unit being configured to perform a coasting lock-up control that when a predetermined coasting lock-up condition is satisfied in a state in which the vehicle is in the coasting travel state, brings the lock-up clutch into a lock-up state, and a first temporary capacity reduction control that when the acceleration ON of the accelerator pedal is judged in a state in which the lock-up clutch is in the lock-up state by the coasting lock-up control, brings the lock-up clutch into a slip state by decreasing the torque transmission capacity (C LU) and subsequently returns the lock-up clutch to the lock-up state by increasing the torque transmission capacity (C LU), ch aracterized in that the control unit is further configured to perform a second temporary capacity reduction control that when the return of the depression of the accelerator pedal is judged during the progress of the returning of the lock-up clutch to the lock-up state by the first temporary capacity reduction control, decreases the torque transmission capacity (C LU) again and subsequently returns the lock-up clutch to the lock-up state again by increasing the torque transmission capacity (C LU), and in the second temporary capacity reduction control, the torque transmission capacity (C LU) being decreased with a predetermined torque transmission capacity by which the lock-up clutch is not fully disengaged being a lower limit value (C LUL). a coasting judgment unit configured to judge whether the vehicle is in a coasting travel state; an acceleration judgment unit configured to judge depression of an accelerator pedal of the vehicle, return of the depression of the accelerator pedal, acceleration ON and acceleration OFF; and a control unit configured to control a torque transmission capacity (C LU) of the lock-up clutch on the basis of judgment information of the coasting judgment unit and the acceleration judgment unit, and the control unit being configured to perform a coasting lock-up control that when a predetermined coasting lock-up condition is satisfied in a state in which the vehicle is in the coasting travel state, brings the lock-up clutch into a lock-up state, and a first temporary capacity reduction control that when the acceleration ON of the accelerator pedal is judged in a state in which the lock-up clutch is in the lock-up state by the coasting lock-up control, brings the lock-up clutch into a slip state by decreasing the torque transmission capacity (C LU) and subsequently returns the lock-up clutch to the lock-up state by increasing the torque transmission capacity (C LU), ch aracterized in that a coasting lock-up control that when a predetermined coasting lock-up condition is satisfied in a state in which the vehicle is in the coasting travel state, brings the lock-up clutch into a lock-up state, and a first temporary capacity reduction control that when the acceleration ON of the accelerator pedal is judged in a state in which the lock-up clutch is in the lock-up state by the coasting lock-up control, brings the lock-up clutch into a slip state by decreasing the torque transmission capacity (C LU) and subsequently returns the lock-up clutch to the lock-up state by increasing the torque transmission capacity (C LU), ch aracterized in that the control unit is further configured to perform a second temporary capacity reduction control that when the return of the depression of the accelerator pedal is judged during the progress of the returning of the lock-up clutch to the lock-up state by the first temporary capacity reduction control, decreases the torque transmission capacity (C LU) again and subsequently returns the lock-up clutch to the lock-up state again by increasing the torque transmission capacity (C LU), and in the second temporary capacity reduction control, the torque transmission capacity (C LU) being decreased with a predetermined torque transmission capacity by which the lock-up clutch is not fully disengaged being a lower limit value (C LUL). a second temporary capacity reduction control that when the return of the depression of the accelerator pedal is judged during the progress of the returning of the lock-up clutch to the lock-up state by the first temporary capacity reduction control, decreases the torque transmission capacity (C LU) again and subsequently returns the lock-up clutch to the lock-up state again by increasing the torque transmission capacity (C LU), and in the second temporary capacity reduction control, the torque transmission capacity (C LU) being decreased with a predetermined torque transmission capacity by which the lock-up clutch is not fully disengaged being a lower limit value (C LUL).