To achieve rapid and reliable prediction of asphalt mixture performance, a method for predicting asphalt mixture performance by optimizing the back propagation (BP) neural network with a genetic algorithm (GA) from the perspective of material composition design was proposed. Initially, a grey relational analysis method was employed to reduce the dimensionality of multidimensional input variables, identifying the core influencing factors of asphalt mixture performance. Subsequently, integrating the GA, a GA-BP neural network prediction model was constructed with the core influencing factors as the input layer and asphalt mixture performance as the output layer. The model underwent training, validation analysis, and prediction generalization application. A comparison with the training effectiveness and prediction accuracy of the BP neural network was conducted to verify the accuracy of the GA-BP neural network model. The research results indicate that the grey relational degrees of eight performance characteristics, including air void, asphalt-aggregate ratio, nominal maximum aggregate size, 4.75 mm passing rate, asphalt type, softening point, penetration, and ductility, are all greater than 0.6, signifying their significant impact on asphalt mixture performance. Compared to the BP neural network model, the GA-BP neural network model reduces the root mean square error (RMSE) by 16% to 31%, decreases the mean absolute error (MAE) by 15% to 24%, and improves the R² value by 0.01 to 0.27, indicating that it has better learning and fitting capabilities. The prediction accuracy for dynamic modulus, dynamic stability, residual stability, splitting tensile strength ratio, and ultimate bending strain of the asphalt mixture is respectively enhanced by 35.26%, 47.78%, 23.13%, 31.92%, and 35.75%, revealing the superior generalization application capability of the GA-BP neural network model. The research findings provide essential references for the rapid prediction of asphalt mixture performance and guidance in the design of asphalt mixture material composition.