A co-evolutionary particle swarm optimization is proposed for multiobjective optimization (MO), in which co-evolutionary operator, competition mutation operator and new selection mechanism are designed for MO problem to guide the whole evolutionary process. By the sharing and exchange of information among particles, it can not only shrink the searching region but maintain the diversity of the population, avoid getting trapped ill local optima which is proved to be effective in providing an appropriate selection pressure to propel the population towards the Pareto-optimal Front. Finally, the proposed algorithm is evaluated by the proposed quality measures and metrics in literatures.