This paper presents a nonlinear robust approach to the slip control problem for a torque converter bypass clutch in a passenger car. The proposed nonlinear robust controller builds upon only the measurements avail-able from inexpensive sensors that are already installed in passenger cars for control. The issue of torque estimation problems for the implementation of the proposed controller is addressed. The stability of the internal dynamics is investigated, upon which a nonlinear robust controller is designed using input-output feedback linearization and Lyapunov redesign technique. The performance of the designed controller is validated by simulation studies.