Radial basis function network (RBF) has excellent generalization ability and approximation accuracy when parameters set properly.However, relying only on traditional methods,it is tough to obtain optimal network's parameters and construct a stabile model as well.In view of this,RBF-MLP neural network is proposed in this article.In the form of connecting two networks to work cooperatively,the RBF's parameter can be adjusted adaptively by the structure of multi-layer perceptron (MLP) so as to realize the effect of backpropagation updating error. Furthermore, genetic algorithm is used to optimize the network's hidden layer so as to confirm the optimal neurons (basis function) number automatically. In addition, a memristive circuit model is proposed to realize the neural network's operation mentioned above based on the character of spin memristors. It is verified that the network can adaptively construct a network model with outstanding robustness and stably achieve 98.33% accuracy in processing the MNIST dataset classification task. The experimental results show that the method mention above has application value.