In this paper, the limitations of conventional BP algorithm were analyzed, and to enhance its generalization capability of the network, the PSO (particle swarm optimization) algorithm was used to optimize the initial weights of nodes in BP neural network and overcome the over-fitting problem and the local minimum problem of the BP neural network. A new algorithm PSO-BP was studied by giving full play to both of the PSO algorithm's global optimization ability and BP algorithm's local search advantage, the model can overcome the slow convergence and easily getting into the local extremum of basic BP algorithm, and can also improve the learning ability and generalization ability with a higher precision. To demonstrate the capacity of the proposed model, we applied the model to the prediction of the fracture acidizing well production. The mean prediction accuracy of the PSO-BP algorithm is 93.56%, and the mean prediction accuracy of the BP algorithm is 87.73%. The results show that the prediction system based on PSO-BP network is more accurate than traditional BP network, so the algorithm based on PSO-BP network model provides a more accurate, safe and reliable result for the fracture acidizing well production prediction.