It is well known that slip control of lock-up clutch in automatic transmission systems is a crucial technology for improving fuel economy and driving comfort. However, plant parameters rapidly vary according to turbine speed, making the slip control challenging. For this problem, we apply nonlinear output regulation theory for the system represented as a linear parameter-varying system with the turbine speed as the parameter. In this framework, it is possible to design a servo controller that is optimally scheduled according to the turbine speed. The effectiveness of the proposed method is confirmed by experiments compared with an $H_{\infty }$ controller, which is one of the most advanced methods employed in the field of lock-up clutch slip control.