Abstract: A Bayesian optimization method based on a Gaussian process model and Thompson sampling is proposed to optimize the performance of a multi-stage compression inlet across a wide Mach number range. The objective function, defined as the specific impulse of the entire thrust tunnel, is evaluated by combining computational fluid dynamics (CFD) simulations of the inlet flow fields and an equivalent thermodynamic process analysis of the engine combustion process. A single-objective optimization at Ma = 6 design point and a three-objective optimization across Ma = 4～6 operating range are carried out. It is found that the mass flow coefficient and total pressure recovery coefficient of the throat are the dominating factors affecting the specific impulse, which does not change monotonously with the total pressure recovery coefficient alone. When the inlet works at the critical back pressure and the combustor operates in a subsonic heating mode, optimal matching is achieved between the inlet and combustor, yielding the highest specific impulse. The optimized design at Ma = 6 point resulted in a 5.66% improvement in specific impulse. Furthermore, the wide-range optimization enhances the flow capture capacity of the inlet and improves the adaptive regulation capability of the separation zone within the internal compression section. By leveraging the choking effect of the aerodynamic throat, the inlet achieves superior matching with the combustor. Accordingly, the specific impulse of the optimized configuration increases by 66.17%, 6.13%, and 4.03% at Ma = 4, 5, and 6 for the entire flow passage, respectively.