A limited number of studies have explored drum brake noise with uncertainty. Therefore, a new method for the robust design of drum brakes is presented herein on the basis of complex modal analysis and Taguchi's robust design. Based on the finite element method, complex modal analysis is used to predict drum brake noise. Taguchi's robust design is adopted to reduce drum brake noise and improve system robustness. In this method, the Young's moduli of the brake drum, brake shoes, and friction lining are considered as control factors, the friction coefficient and brake pressure are taken as noise factors, and the weighted instability tendency coefficient is regarded as the objective function. When the proposed method is applied to drum brake design, drum brake noise is significantly reduced and system robustness is increased. Specifically, the signal-to-noise ratio increases by 62.94%, and the average value of the weighted instability tendency coefficient decreases by 91.7%.