The computational contact mechanics methods for the spur gears, such as the finite element method, are time-consuming and difficult to deal with the dynamic contact stress. For rapidly solving the gears dynamic contact stresses, a dynamic stress predicting method for the spur gears should be proposed based on the BP neural network. Firstly, the spur gears stress distribution at different meshing point should be calculated with the finite element method. Then the nodes stresses on the tooth surfaces are extracted to reduce computing complexity. While the multi-neuron two-layer BP neural network surrogate model is built, the time-varying contact stresses of the spur gears can be predicted with the extractive tooth surfaces nodes stresses which the R2 of the results can achieve to 0.94. Finally, comparing with the predictive contact stresses of spur gears via the RBF model, the random forest model and the Kriging model, the results show that this work with BP neural network is more accuracy, lower computational costs as well as the fast computation method.