Based on the existing results of wavelet neural networks， a new neural network based on wavelet packet theory is presented. The new network extracts best wavelet packet basis as activation function of its neuron and determines network's structure and number of nodes according to time-frequency approximation principle. An improved algorithm of velocity tracking particle swarm optimization（VTPSO） is used to train connection weights of the network， which overcomes the defects of traditional learning algorithm such as slow convergence rate and easy to fall into local minimum. The structure design and parameter learning method of the network are introduced and the simulation experiment proves that the network can approximate nonlinear system accurately and rapidly. The new neural network is applied in identifying power amplification of power system fault recurrence device to establish the input-output model of device. By comparing the model's output with ideal amplifying value， the fault recording data is modified in numeric area before being recurred by the device， which solves the fault recurrence wave's nonlinear error problem effectively.