The design of lightweight automotive structures has become a prevalent practice in the automotive industry. This study focuses on design optimization of an automobile torque arm subjected to cyclic loading. Starting from an available initial design, the shape of the torque arm is optimized for minimum weight such that the fatigue life of the torque arm does not fall below that of the initial design and the maximum von Mises stress developed in the torque arm does not exceed that of the initial design. The stresses are computed using ANSYS finite element software, and the fatigue life is calculated using the Smith-Watson-Topper model. Surrogate-based optimization approach is used to reduce the computational cost. Optimization results based on global surrogate modeling and successive surrogate modeling approaches are compared. It is found that the successive surrogate modeling approach results in 28.7% weight reduction for the torque arm, whereas the global surrogate modeling approach results in 25.7% weight saving for the torque arm.