This paper presents a method to estimate the all-terminal reliability of network by neural networks. We first employ the scheme that a network topology is mapped into a binary vector, and use Monte Carlo simulation to obtain sample data of network reliability. Then the neural networks are constructed, trained and validated with the network topologies, links reliabilities and data set of network reliability. A grouped cross-validation approach is adopted to improve the performance of neural networks. The results show the model can carry out the non-linear mapping relationship between the topological structure, the links reliabilities and the reliability of network.