‘Moan’ noise in a vehicle causes discomfort and anxiety to passengers. In the previous study, the causes of moan noise were identified, and a coherence analysis of the components was conducted. It was found that moan noise was generated by the attribution of resonance when the exciting force produced by the stick–slip motion in a brake system was transmitted to a coupled torsional beam axle module. The analysis involved calculation of the response of the coupled torsional beam axle module on a full suspension brake system reconstructed by consideration of the transfer functions and the joint conditions of the coupled torsional beam axle module and the brake system. Each transfer function is decomposed by a frequency-response-function-based substructuring technique. In this study, when using the sensitivity analysis and optimization techniques for moan-noise reduction, the frequency-response-function-based substructuring technique was performed to calculate the response of the modified coupled torsional beam axle module by considering the joint conditions and the transfer functions of the brake system. Highly sensitive design parameters regarding the response of the coupled torsional beam axle module were identified after the sensitivity analysis. The most sensitive design parameters were selected to enhance the efficiency and the robustness of optimization. The optimal values for the design variables were obtained by applying a progressive quadratic response surface method as a optimization algorithm. The application of an optimization technique was possible using the finite element model and the results of the finite element analysis from the previous study. After optimization, a prototype was re-designed, manufactured and tested. Finally, it was verified that the moan noise was reduced, as the natural frequency of 387 Hz for the coupled torsional beam axle module was moved to a higher frequency.