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The forecast of the stock index fluctuation is a difficult job as it is influenced by many factors. In recent years, back propagation neural network (BPNN) has been applied in stock index prediction. However, in practical application, BPNN has some disadvantages. The widely used BP learning algorithm has slow convergent speed and low learning efficiency, and it is easy to get in local minimum. The inheritance algorithm is a sort of self-adaptive optimized search algorithm based on natural selection and natural inheritance. It can be implemented in different areas of parameter space in the colony generation subrogation toward the optimal direction which the search could more possibly find and couldnpsilat get in local minimization. So, we can adopt the inheritance algorithm to train the BP neural network to overcome the above disadvantages. We optimized the network through adding inheritance algorithm and established the stock index prediction model to predict Shanghai composite index. The empirical analysis indicated that the above model optimized with inheritance algorithm possessed better function approximating ability, and achieved ideal effect for the short-term prediction of stock index.