Back propagation (BP) neural networks are very effective approaches for machine learning, classification, and prediction. This thesis focus on BP neural networks, especially on their application to analysis of contribution rates and predictions. Contribution rates are calculated with the weight matrix of BP neural network and prediction is achieved with a hybrid model composed of BP neural network and time series model. To overcome the disadvantages of traditional BP neural networks, improved gradient methods are used, for example, Levenberg-Marquardt (LM) method and gradient descent with adaptive learning rate & momentum method, which can accelerate training speed and avoid local minimum. In numerical experiments, the contribution rates of stock indicators to stock price are calculated and the results are compared with variable selection result of stepwise regression method. Comparison result indicates that BP neural network method is an effective way to calculate contribution rates. And a strategy is proposed to apply the hybrid prediction model to actual stock market. The results indicate that the hybrid model works well and the strategy is effective.