Many real-world problems in engineering and process synthesis tend to be highly dimensional and nonlinear, even involve conflicting multiple objectives and subject to many constraints, which makes the feasible regions narrow; hence, it is hard to be solved by traditional constraint handling techniques used in evolutionary algorithms. To handle this issue, this paper presents a multi-objective differential evolution with dynamic hybrid constraint handling mechanism (MODE-DCH) for tackling constrained multi-objective problems (CMOPs). In MODE-DCH, global search model and local search model combined with different constraint handling methods are proposed, and they are executed dynamically based on the feasibility proportion of the population. In the early stage that the feasible ratio is low, the local search model focuses on dragging the population into feasible regions rapidly, while the global search model is used to refine the whole population in the later stage. The two major modules of the algorithm cooperate together to balance the convergence and distribution of Pareto-optimal front. To demonstrate the effectiveness of MODE-DCH, the proposed algorithm is applied on several well-known CMOPs and two engineering problems compared with two other state-of-the-art multi-objective algorithms. The performance indicators show that MODE-DCH is an effective method to solve CMOPs.