In the real world, many optimization problems are dynamic constrained multi-objective optimization problems. This requires an optimization algorithm not only to find the global optimal solutions under a specific environment but also to track the trajectory of the varying optima over dynamic environments. To address this requirement, this paper proposes a novel particle swarm optimization algorithm for such problems. This algorithm employs a new points selection strategy to speed up evolutionary process, and a local search operator to search optimal solutions in a promising subregion. The new algorithm is examined and compared with two wellknown algorithms on a sequence of benchmark functions. The results show that the proposed algorithm can effectively track the varying Pareto fronts over time. The proposed developments are effective individually, but the combined effect is much better for the test functions.