To address the problem that constrained multi-objective optimization cannot balance objective optimization and constraint satisfaction while maintaining population diversity and convergence, this study proposes a constrained multi-objective wolf pack algorithm embedded with an adaptive epsilon constraint handling mechanism (MOWPA-AE). Firstly, the adaptive constraint-handling mechanism divides the population evolution process into a learning stage and an exploration stage. In the learning stage, a small number of feasible solutions and high-quality infeasible solutions are used to guide the population toward rapid convergence. In the exploration stage, stronger constraints are imposed on the converged population, and non-dominated feasible solutions are used to diffuse and search for the constrained Pareto front, thereby balancing convergence, diversity, and constraint satisfaction. Secondly, an elite-guided strategy is designed to promote a uniform distribution of solutions in the search space and enhance global search capability. Finally, a differential evolution update mechanism is introduced, which selects superior individuals through a binary tournament and performs differential mutation, accelerating evolution while maintaining diversity. Comparative experiments on 20 constrained multi-objective test functions and the welded beam engineering problem demonstrate that the MOWPA-AE not only exhibits excellent overall performance in constraint satisfaction and objective optimization but also shows feasibility and potential for application in practical engineering optimization problems.