To cope with the limitations of the grey wolf optimization (GWO) algorithm in accuracy of optimization accuracy and speed of convergence, this paper proposes an upgraded algorithm called SL-Relu Adaptive Grey Wolf Optimizer (SAGWO), which combines SL-Relu inertia weight and improved fitness coefficient. SAGWO improves the search efficiency of the GWO algorithm by integrating the inertia weight strategy of the SL-Relu function and the improved fitness coefficient. According to the comparative consequences of six test functions, compared with seven traditional swarm intelligence algorithms, SAGWO has faster convergence speed, higher accuracy, and robustness. In addition, this paper also explores the application of SAGWO in optimizing the BP neural network and shows its advantages in improving price prediction accuracy and accelerating convergence. In particular, when dealing with complex data sets, SAGWO demonstrates significant performance advantages, which proves its effectiveness and potential value in practical application.