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Artificial neural network (ANN) algorithm has the advantages of fast computing speed, strong self-learning ability, good robustness and so on. However, due to the lack of theoretical support for the selection of initial parameters and activation function, it often leads to slow convergence speed and local extreme value, thus affecting the convergence and generalization ability of the whole neural network. Based on the basic theory of fracture mechanics, an improved activation function algorithm of BP neural network with enrichment is proposed. In this research, to combine the advantages of the numerical methods and the ANNs, an improved back propagation neural network (BPNN) is proposed through introducing the enrichment used in the numerical methods into the activation function utilized in the neural networks. The enrichment is able to represent the crack tip field which can accelerate the convergence. At the field near the crack tip, the improved BP solution can converge to the analytical solutions which validate the high accuracy of the proposed method. Without sufficient data, especially the data are missing in the near field of the crack tip, the improved BP method can also achieve high accuracy and convergence, while the conventional BP method may not converge to the predetermined error bound. Numerical simulations of the quasi-static and fatigue crack problems demonstrate that the improved BP method can accurately predict the crack propagation and its growth rate with relatively little data.