A self-organizing radial basis function(RBF) neural network(SODM-RBFNN) was presented for predicting the production yields and operating optimization. Gradient descent algorithm was used to optimize the widths of RBF neural network with the initial parameters obtained by k-means learning method. During the iteration procedure of the algorithm, the centers of the neural network were optimized by using the gradient method with these optimized width values. The computational efficiency was maintained by using the multi-threading technique. SODM-RBFNN consists of two RBF neural network models: one is a running model used to predict the product yields of fluid catalytic cracking unit(FCCU) and optimize its operating parameters; the other is a learning model applied to construct or correct a RBF neural network. The running model can be updated by the learning model according to an accuracy criterion. The simulation results of a five-lump kinetic model exhibit its accuracy and generalization capabilities, and practical application in FCCU illustrates its effectiveness.