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, a hyper rectangle search based particle swarm algorithm is proposed for such problems. This algorithm employs a hyper rectangle search to predict the optimal solutions (in variable space) of the next time step. Then, a PSO based crossover operator is used to deal with all kinds of constraints appearing in the problems when the time step (environment) is fixed. This algorithm is tested and compared with two well known algorithms on a set of benchmarks. The results show that the proposed algorithm can effectively track the varying Pareto fronts over time.