In the plastic injection molding (PIM), the optimization of the process parameters is a complex task. The objective of this study is to propose an intelligent approach for efficiently optimizing PIM parameters when multiple objectives are involved, where different objectives, such as minimizing part weight, flash, or volumetric shrinkage, present trade-off behaviors. Multiple objective functions reflecting the product quality are constructed for the optimization model of PIM parameters. The proposed approach integrates Taguchi's parameter design method, back-propagation neural network (BPNN), grey correlation analysis (GCA), particle swarm optimization (PSO) and multiobjective particle swarm optimization (MOPSO) to locate the Pareto optimal solution for multiobjective optimization problem. PSO and GCA are applied to optimize the network structure of BPNN to establish multiobjective mathematical model (PSO-GCANN) that finely maps the relationship between the input process parameters and output multiresponse. MOPSO is used to fine-tune the Pareto optimal solutions while the approximate PSO-GCANN is utilized to efficiently compute the fitness of every individual during the evolution of MOPSO. The illustrative application and comparison of results show that the proposed methodology outperforms the existing methods and can help mold designers to efficiently and effectively identify optimal process parameters.