Magnetorheological (MR) brakes provide variable friction torque by electronically changing the viscosity of a magnetic fluid inside the actuator. The MR-brakes have many desirable characteristics, such as high torque-to-volume ratio, inherent stability and ease of control. However, the design process of such an actuator is complex and time consuming due to many parameters involved in the design, including geometric and physical factors and their interactions. The first contribution of this research is a new optimization approach where we combined the Taguchi optimization method with parameterized magnetic finite element analysis. Unlike other optimization techniques, this method can identify the dominant parameters of the design and investigate their interactions with the design output while reducing the search space and the design time. The second contribution is the design optimization of a novel MR-brake, which incorporates a serpentine flux path and a permanent magnet. To the best of our knowledge, this is the first such MR-brake. The new MR-brake design provides a fail-safe feature while reducing the volume by decreasing the number of coil turns required. Results showed that some of the geometric parameters and the current have the most significant effect on the torque output out of the 12 design parameters.