In order to realize the over fitting problem existing in Back Propagation (BP) neural networks, a neural prediction model based on Pearson correlation was designed. It replaces the error function in a BP neural network based on error back propagation with the Pearson correlation function. By means of gradient ascent, the adjustment of connection weights and biases in training process is derived. Meanwhile, momentum is added to this adjustment to improve the convergence speed of the network. The Pearson correlation BP prediction model is built with weight threshold limiting and an increasing learning rate to prevent overfitting. Time series prediction experiments on a standard dataset were performed. The results demonstrate that compared with improved the radial basis function and BP neural networks, the Pearson correlation BP neural network reduces root-mean-square error, and time to convergence in multi-factor time series prediction. Therefore, the Pearson correlation BP neural network realizes the integration of correlation analysis with neural networks, is able to ensure efficiency, and can solve fitting problems in the same time as other methods with higher accuracy.