In the selective laser melting (SLM) process, the experimental approach to determine the optimal process parameters is labor-intensive, material-intensive, and time-consuming. The use of simulation methods also requires more time support and higher hardware requirements. In this paper, a three-dimensional transient heat transfer model and a neural network optimization process parameter model in the process of preparing copper alloys by SLM are developed by combining finite element simulation methods with neural network prediction. The thermal behavior of the multitrack molten pools was investigated by ANSYS APDL, and the effects of different laser powers and scanning speeds on the temperature field and structure dimensions of the molten pools were discussed. The results show that the current single-track has a significant preheating effect on the unmachined single-track and a reheating effect on the machined single-track during the multitrack forming process. The laser power and scanning speed can be controlled to regulate the temperature, 3D size, and heat spread area of the molten pool to avoid over-melting and under-melting. The accuracy of the temperature field model was verified by single-track experiments. A neural network prediction model was constructed to predict the maximum temperature and size of the molten pool by optimizing the backpropagation neural network with a genetic algorithm, providing a methodological guide for the study of SLM process parameters.