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Due to the limitations of existing optimization algorithms in global optimization, neural networks require multiple trainings to obtain satisfactory results. In order to solve the consistency problem of neural network training, this paper proposes an adaptive parallel structure neural network (APSNN). APSNN consists of multiple neural network units in parallel, and each neural network unit is trained using conventional optimization algorithms during the training process. The training samples of the neural network unit are composed of the training residuals of the previous neural network unit. Through the one-way transmission of the training residuals in each neural network unit, the training residuals are gradually reduced. According to the training residuals, the neural network decides whether to cascade the neural network units and expand the structure, so as to ensure the consistency of the training results. The neural network approximation test is carried out on five nonlinear functions in this paper. Compared with BP neural network, APSNN has very stable training accuracy and good consistency under 50 different initial conditions. In order to predict traffic flow, this paper compares APSNN with BP neural network and wavelet neural network. The results show that the overall standard deviation of APSNN prediction is smaller than that of BP neural network and wavelet neural network, and the prediction deviation of traffic flow is 2.7% and 9.7% lower than that of BP neural network and wavelet neural network, respectively.