Solving multi-objective optimization problems through meta-heuristic methods gets considerable attention. Based on the classical variation operators, several enhanced operators, as well as multi-objective optimization evolutionary algorithms, have been developed. Among these operators, the competitive swarm optimizer exhibits promising performance. However, it encounters difficulties when tackling constrained multi-objective optimization problems with large objective spaces or complex infeasible regions. In this paper, a competitive and cooperative swarm optimizer is proposed, which contains two particle update strategies: i) the competitive swarm optimizer provides faster convergence speed to accelerate the approximation of the Pareto front; and ii) the cooperative swarm optimizer suggests a mutual-learning strategy to enhance the ability to jump out of local feasible regions or local optima. We also present a new algorithm for constrained multi-objective optimization problems. The results on four benchmark suites with 47 instances demonstrate the superiority of our approach compared with other state-of-the-art methods. Additionally, its effectiveness on large scale constrained multi-objective optimization problems has also been verified.