In this study, to accurately predict the temperature and melting ratio at low time and cost, the process of dissimilar laser welding of stainless steel 304 and copper was simulated based on artificial neural network (ANN). Among various ANN models, the Bayesian regulation backpropagation training method was utilized to model the current problem. This method was used considering the two temperatures of copper and steel and the two melting ratios of steel and copper as the four outputs, and the four parameters, pulse width, pulse frequency, welding speed, and focal length, as the inputs. According to the results, regression values had a good accuracy in all cases and the histogram diagrams indicated that the error distribution was mainly concentrated at the center; in other words, the major errors of the network were not very large. It was also observed that the error concerning the trained neural networks was acceptable in the experiment phase. Finally, this neural network could be used as a numerical model to estimate the four outputs of steel temperature, copper temperature, steel melting ratio, and copper melting ratio for all input values of pulse width, pulse frequency, welding speed, and focal length in the studied range, without any need to rerun the experiment.