In order to achieve accurate prediction of surface roughness of magnetic abrasive finishing, the precision prediction model of surface roughness by BP neural network optimized by genetic algorithm was established. Taking the surface roughness as the target of prediction, five main process parameters affecting the inner surface quality of 5052 Al alloy tube by magnetic abrasive finishing as inputs of neural network. Through the orthogonal experimental design, the surface roughness under different process parameters was obtained as the output of the neural network. By establishing a nonlinear prediction model, the prediction effect of surface roughness before and after optimization was analyzed by comparing the mean square error and simulation time of the optimized genetic algorithm and the traditional BP neural network. Based on experimental data, the BP neural network with 5-11-1 topology structure is established. The mean square deviation of the prediction model is 0.044, the simulation time is 0.187 s, and the average relative error rate is 13.2%. The mean square deviation of the unoptimized BP neural network prediction model is 0.231, and the simulation time is 1.840 s. The mean square error of evolutionary BP neural network is smaller, and the modeling and simulation time is shorter, and more accurate prediction by evolutionary BP neural network can be achieved. What’s more, the BP neutral network can greatly avoid the disadvantage of traditional BP neural network easily falling into local minimum.