Abstract: FCCU(fluid catalysis and cracking unit) is a highly non-linear, time variable, long time delay, intensive coupling, parameter distributed, indefinite and complex system. A fuzzy neural network based on the process mechanism for the modeling has been established. The autocorrelation function checking method to test the correctness of the model, and the advanced Frank-Wolfe algorithm are used to compute stable state optimization. An oil refinery works FCCU is also used to test and study the system identification, modeling and stable state optimal control by the network. The fuzzy neural network (FNN) has such advantages as multiple hidden layers, multiple neurons in each hidden layer, strong generalization and approximation ability, quick convergence rate, etc. Moreover we can make differential calculation to the input variables by output variables, which makes optimization calculation convenient. The fuzzy neural network, working with the advanced Frank-Wolfe algorithm, can be used in system modeling and stable state optimal control of non-linear complex production process.