A heat-exchanger/reactor (HEX reactor) is a kind of plug-flow chemical reactor which combines high heat transfer ability and chemical performance. It is a compact reactor designed under the popular trend of process intensification in chemical engineering. Previous studies have investigated its characteristics experimentally. This paper aimed to develop a general numerical model of the HEX reactor for further control and diagnostic use. To achieve this, physical structure and hydrodynamic and thermal performance were studied. A typical exothermic reaction, which was used in experiments, is modeled in detail. Some of the experimental data without reaction were used for estimating the heat transfer coefficient by genetic algorithm. Finally, a non-linear numerical model of 255 calculating modules was developed on the Matlab/Simulink platform. Simulations of this model were done under conditions with and without chemical reactions. Results were compared with reserved experimental data to show its validity and accuracy. Thus, further research such as fault diagnosis and fault-tolerant control of this HEX reactor could be carried out based on this model. The modeling methodology specified in this paper is not restricted, and could also be used for other reactions and other sizes of HEX reactors.