This paper presents an optimal design of a magnetorheological(MR) fan clutch based on finite element analysis and also presents torque control of engine cooling fan using a sliding mode control. The MR fan clutch is constrained in a specific volume and the optimization problem identifies the geometric dimension of the fan clutch that minimizes an objective function. The objective function for the optimization problem is determined based on the solution of the magnetic circuit of the initially designed clutch. Under consideration of spatial limitation, design parameters are optimally determined using finite element analysis. After describing the configuration of the MR fan clutch, the viscous torque and controllable torque are obtained on the basis of the Bingham model of MR fluid. Then, a sliding mode controller is designed to control the torque of the fan clutch according to engine room temperature and control performance is evaluated through computer simulation.