Shallow models have limited ability to express high-dimensional nonlinear complex functions. Based on deep learning, a Gaussian radial basis function neural network (RBFNN) is proposed, which is an analysis method of nonlinear complex function approximation based on the Gaussian-RBFNN model. The proposed method can approximate single-variable and binary complex nonlinear functions, and the approximation error is less than 0.1, which can achieve the ideal approximation effect. Finally, the proposed method is applied to analyze the nonlinear complex stock prediction approximation problem, and the effectiveness and practicality of the method are further verified. It can be seen that compared with the BP neural network model, this model performs better in average training time, training standard error, Ratt, RATR, and trmse For RBFNN; the training only needs 50 iterations, while the traditional BP needs 7100 training to gradually converge. In the actual function test, after 275 times of training, the convergence speed gradually tends to be stable, and the predicted value is closer to the actual value. Therefore, the model can be used to analyze practical nonlinear complex function approximation problems.