Many artificial neural networks are the simple simulation of brain neural network's architecture and function. However, how to rebuild new artificial neural network which architecture is similar to biological neural networks is worth studying. In this study, a new multilayer feedforward small-world neural network is presented using the results form research on complex network. Firstly, a new multilayer feedforward small-world neural network which relies on the rewiring probability heavily is built up on the basis of the construction ideology of Watts-Strogatz networks model and community structure. Secondly, fault tolerance is employed in investigating the performances of new small-world neural network. When the network with connection fault or neuron damage is used to test the fault tolerance performance under different rewiring probability, simulation results show that the fault tolerance capability of small-world neural network outmatches that of the same scale regular network when the fault probability is more than 40%, while random network has the best fault tolerance capability.