It is well known that a good method for improving fuel economy is to engage the lock-up clutch of the torque-converter. In the lock-up clutch, it is necessary to control the slip speed from lower speed region in order to improve fuel consumption performance. In the control system of the lock-up clutch, there is a case in which a rate limiter is inserted in the control input to reduce a shock or an uncomfortable feeling to drivers when the lock-up clutch is connected. However, the rate limiter may cause a windup effect that degrades a control performance. Thus, in this paper, we apply three anti-windup methods to the control system of the lock-up clutch, and the effectiveness of each method is evaluated by simulations.