In recent years, DNA computing model has gradually attracted attention due to its low energy consumption, high capacity of storing information and good parallelism. DNA computational model is calculated by DNA molecule as the medium, so its core is to design a high quality DNA sequence conforming to various constraints. Designing DNA sequences that meet a series of constraints, such as temperature, H-measure, and continuity, is a typical multi-objective optimization problem. In traditional multi-objective optimization problems, various fitness functions are usually only related to their own solutions, and have no correlation with other redundant candidate solutions. Based on the DNA coding problem's characteristics, we propose a two-stage constrained multi-objective evolutionary algorithm. Our algorithm overcomes shortcomings of traditional algorithms in solving DNA coding problems which are easy to fall into local optimal solutions. Experimental results demonstrate that our algorithm is effective and reliable in solving DNA coding problems when compared to other mainstream algorithms from recent years.