Balancing objectives optimization and constraints satisfaction are two equally important goals for constrained multi-objective optimization problems (CMOPs). However, most studies pay more attention on avoiding violating the constraints than achieving better objectives optimization. To alleviate this issue, this paper presents a dynamic constrained multi-objective evolutionary algorithm (DCMOEA) for handling constraints and optimizing objectives simultaneously. DCMOEA converts a m-objective COP to a dynamic (m+2)-objective COP. A simple yet effective dynamic niching technique is designed to enhance the population diversity from the decision space. An instantiation of the DCMOEA on NSGA-II (named DCNSGA-II) is implemented, and compared with five representative constraint-handling techniques on 26 well-known CMOPs. The experimental results indicate that the DCNSGA-II is highly competitive in solving CMOPs.