Community discovery is an important task in mining complex networks, and has important theoretical and application value in the terrorist organization identification, protein function prediction, public opinion analysis, etc. However, existing metrics used to measure quality of network communities are data dependent and have coupling relations, and the community discovery algorithms based on optimizing just one metric have a lot of limitations. To address the issues, the task to discover network communities is formalized as a multi-objective optimization problem. An algorithm, MOCD-PSO, is used to discover network communities based on multi-objective particle swarm optimization, which constructs objective function with modularity Q, MinMaxCut and silhouette. The experimental results show that the proposed algorithm has good convergence and can find Pareto optimal network communities with relatively well uniform and dispersive distribution. In addition, compared with the classical algorithms based on single objective optimization (GN, GA-Net) and multi-objective optimization (MOGA-Net,SCAH-MOHSA), the proposed algorithm requires no input parameters and can discover the higher-quality community structure in networks.