In a lock-up clutch control device, base hydraulic pressure calculation device calculates base hydraulic pressure Pb for engaging a lock-up clutch based on input torque from an engine, correction factor calculation device calculates correction factor α, which is greater than 0 but less than 1, for correcting the base hydraulic pressure Pb based on an input rotational speed Ni of a transmission and a cylinder cut-off state of the engine. Commanded hydraulic pressure calculation device calculates a commanded hydraulic pressure Pc from the base hydraulic pressure Pb and the correction factor α by means of: current value of commanded hydraulic pressure Pc←previous value of commanded hydraulic pressure Pc+(base hydraulic pressure Pb−previous value of commanded hydraulic pressure Pc)×α, and the commanded hydraulic pressure Pc is made to converge to the base hydraulic pressure Pb by repeating this a predetermined number of times.