Due to the influence of injection molding process, warpage and volume shrinkage are two common quality defects for products manufactured by the glass fiber-reinforced plastic (GFRP) injection molding. In order to minimize the two defects, the extreme learning machine optimized by genetic algorithm (GA-ELM), multi-objective firefly algorithm (MOFA) and a multi-objective decision-making method called GRA-TOPSIS are implemented in this study. All experiments based on Latin hypercubic sampling (LHS) are conducted by Moldflow software to obtain results of warpage and volume shrinkage. The prediction accuracy of defect prediction models based on the extreme learning machine (ELM) and GA-ELM algorithm is compared. The results show that GA-ELM models can better predict defect values. Finally, MOFA is utilized to find the Pareto optimal front, and the GRA-TOPSIS method is used to find the optimum solution from the Pareto optimal front. According to the results of the simulation verification, the warpage and volume shrinkage are effectively reduced by 12.25% and 6.11% compared with those before optimization, respectively, which indicates the effectiveness and reliability of the optimization method.