The existing performance prediction model of asphalt pavements is limited by low accuracy and a lack of historical measured data. To address this issue and maximally optimize the pavement maintenance decision, a pavement performance prediction model integrating particle swarm optimization (PSO), gray model (GM), and back propagation neural network (BPNN) was proposed based on network management. Meanwhile, the model was compared with the GM(1,1) model, support vector regression (SVR) model, BPNN model, and PSO-BPNN model. Then, the prediction accuracy of the models was evaluated by the mean absolute error (E_MAE), the root mean square error (E_RMSE), and the mean absolute percentage error (E_MAPE). The fitting results of the PSO-gray BPNN model were assessed by the R-squared (R²). The results indicate that by optimizing the BPNN model with the PSO algorithm and the GM model, the accuracy of the PSO-gray BPNN model is significantly improved. Based on the performance data of 14 expressways in Hubei Province, a high correlation between the predicted values of the model and the measured data is found. For the I_PCI index, the value of E_MAE, E_RMSE, and E_MAPE is reduced to 1.721 8, 2.296 8, and 1.897 1, respectively. The value of R² could be up to 0.919. Compared to the other four models, the PSO-gray BPNN model has the smallest values of prediction error for I_PCI, I_RQI, I_RDI, and I_SRI, fully showing the superiority of the model. With higher prediction accuracy, the proposed PSO-gray BPNN model has prediction results more consistent with the actual situation, providing an accurate and reliable technical support for the prediction of pavement performance at the network level.