To effectively simulate the combustion of hydrogen/hydrocarbon-fueled supersonic engines, such as scramjet and rocket-based combined cycle (RBCC) engines, a detailed mechanism for chemistry is usually required but computationally prohibitive. In order to accelerate chemistry calculation, an artificial neural network (ANN) based methodology was introduced in this study. This methodology consists of two different layers: self-organizing map (SOM) and back-propagation neural network (BPNN). The SOM is for clustering the dataset into subsets to reduce the nonlinearity, while the BPNN is for regression for each subset. Compared with previous studies, the chemical reaction mechanism involved in this study is more complex, therefore, the particle swarm optimization (PSO) method is employed for accelerating training process in this study. Then we were committed to constructing an ANN-based mechanism of hydrogen and kerosene for supersonic turbulent combustion and verifying it in a practical RBCC combustion chamber. The training data was generated by RANS simulations of the RBCC combustion chamber, and then fed into the SOM-BPNN with six different topologies (three different SOM topologies and two different BPNN topologies). Through LES simulation of the Rocket-Based Combined Cycle (RBCC) combustor, the six ANN-based mechanisms were verified. By comparing the predicted results of six cases with those of the conventional ODE solver, it is found that if the topology is properly designed, high-precision results in terms of ignition, quenching and mass fraction prediction can be achieved. As for efficiency, 8~20 times speedup of the chemical system integration was achieved, which will greatly improve the computational efficiency of combustion simulation of hydrogen/carbon monoxide/kerosene mixture.