The injection molding process has been widely used as the most important manufacturing process for plastic-based products. The objective of the current study is to simulate and optimize the injection molding process parameters for a computer-fan frame product using Taguchi method and grey correlation analysis. Before the simulation, the 3D model of the computer-fan frame product was first designed using NX software. Then, Moldflow was used to simulate the filling times, flow front temperature, clamping forces, and welding line for determining the optimal positions of injecting gates. Taguchi method was then applied, and four processing parameters including mold temperature, melt temperature, filling pressure, and packing time were considered as the parameters for the determination of warpage deformation and volumetric shrinkage. The analysis of variance was applied to optimize the parameters with the minimum warpage deformation and volumetric shrinkage. The grey correlation analysis was applied for multi-objective optimization of warpage deformation and volumetric shrinkage. Results show that the filling pressure and melting temperature have a significant effect on the volumetric shrinkage and warpage deformation. The single-objective optimization of volumetric shrinkage and warpage deformation are 10.66% and 0.648 mm, respectively, and the multi-objective optimization of volumetric shrinkage and warpage deformation are 10.88% and 0.646 mm, respectively. The results also indicate that the Taguchi method and the grey correlation analysis could be applied to obtain the optimal combination of injection molding process parameters.