A lock-up control device is provided to control the engaging and release of a lock-up clutch, which is arranged in parallel with a torque converter to transmit driving force of an engine of a car. Herein, target driving force is calculated based on accelerator pedal opening and car velocity. A present shift position is detected using a shift map based on accelerator pedal opening, car velocity and engine speed. Target engine torque is calculated based on the target driving force and present shift position as well as a torque amplification ratio, which is detected when the torque converter is placed in a torque amplification state. A lock-up release instruction is issued under conditions that the torque converter is placed in the torque amplification state while the target engine torque is greater than a preset value, which is determined in advance based on a torque characteristic of the engine. In addition, under the condition that the engaging of the lock-up clutch is released, the device makes a decision as to whether a shift-down operation is performed or not. Herein, accumulation is performed on the accelerator pedal opening under the condition that the target engine torque is greater than the preset value. So, a shift-down instruction is issued under the condition that an accumulated value of the accelerator pedal opening exceeds a threshold value in accumulation of the accelerator pedal opening.