ECG recorders are precision medical devices, but their thin-walled shells are susceptible to warpage and shrinkage during injection molding production due to the injection molding process, which greatly shortens their service life. To address this problem, a multiobjective optimization method for injection molding process parameters based on a combination of a BP neural network model optimized by an ant colony algorithm (ACO-BP) and an improved non-dominated sorting genetic algorithm (NSGA-II) is proposed. The study takes the warpage deformation amount and volume shrinkage rate of the plastic part as the optimization objectives, and the melt temperature, mold temperature, injection pressure, holding pressure, holding time, and cooling time as the design variables. However, for BP neural networks, it is crucial to choose an appropriate number of hidden layer neurons, so the particle swarm algorithm combined with the grey wolf algorithm (GWO-PSO) is used to solve for the optimal number of hidden layer neurons. Firstly, the number of hidden layer neurons of the BP network model was solved based on the samples obtained from the Box–Behnken experimental design and the GWO-PSO algorithm, and the ACO-BP algorithm was used to build the prediction models for warpage and volume shrinkage, respectively, and then combined with NSGA-II for global optimisation. The pareto optimal solution set was subjected to CRITIC analysis and the optimal process parameters were finally obtained, with a minimum warpage of 0.3293 mm and minimum volume shrinkage of 4.993%, a reduction of 8.93 and 6.95% respectively compared to the pre-optimisation period. At the same time, injection molding tests were carried out on the optimum process parameters, and it was found that the molding quality of the plastic parts was better and met the actual production requirements through measurement. The research in this paper provides a theoretical basis for further improving the quality defects of the thin-walled injection molded parts.