As the central element of the cathode air supply system, the centrifugal air compressor is pivotal to the regular and efficient operation of on-board fuel cells. In an attempt to further enhance the overall properties of the air compressor, the computational fluid dynamics (CFD) simulation model and Stacking model are developed and calibrated in this study. On this basis, the Many-Objective Random Walk Gray Wolf Optimizer (MORW-GWO) algorithm is proposed to perform many-objective optimization for compressor structural parameters, and the intrinsic mechanisms of performance improvements are elaborated based on three-dimensional flow analysis. The results indicate that the Stacking model achieves excellent predictive performance and generalization ability through the coupling and mutual error correction of base learners and the meta-learner. The MORW-GWO algorithm demonstrates outstanding many-objective optimization capability, convergence ability and universality. Compared to the original compressor, the optimized air compressor achieves improvements of 2.8%, 2.3%, 9.3% and 16.0% in the pressure ratio, outlet temperature, isentropic efficiency and adiabatic compression work, respectively. Besides, it is found that the internal energy loss, separation loss, friction loss, gas leakage and backflow of the optimized air compressor are reduced through the 3-D flow characteristic analysis. The findings can contribute to the many-objective optimization of compressor structural parameters by giving theoretical guidance, data support and directional evidence.