This paper presents a servo control method for the multiple launch rocket system (MLRS) launcher during marching fire operations. The MLRS, being a complex nonlinear system, presents challenges in designing its servo controller. To address this, we introduce the fuzzy adaptive sliding mode control (FASMC) approach. The permanent magnet synchronous motor (PMSM) and controller of the MLRS were simulated in the MATLAB/Simulink environment. The dynamic model of the MLRS during marching fire was established using multi-body system theory, vehicle mechanics, and launch dynamics. The dynamic model was then integrated with the FASMC-based controller using the Adams/View module. Numerical calculations were performed to demonstrate the control performance and the effectiveness and applicability of the proposed approach were validated through a comparison experiment between FASMC and other common control methods.