A dynamic simulation model of a hybrid power generation system of a solid oxide fuel cell and a homogeneous charge compression ignition engine was developed to investigate the behavior of the system during the start-up process. The stack, reformer, catalytic burner, and heat exchanger were implemented as dynamic models based on physical equations. For the engine, an experimental data-based mapping model was developed. The dynamic model was simulated on a Matlab/Simulink platform. Individually developed component models were assembled as an integrated system model and operated at the system level. The hybrid system was designed to generate approximately 4 kW of electricity from the SOFC stack and 1 kW from the engine, resulting in a total system power of 5 kW, with an electrical efficiency of 50.6%. The integrated model was operated using a four-step start-up procedure for 50 h, during which the temperature and composition of the stream were observed in time. Based on this, the dynamic behavior of the system was analyzed at each stage throughout the entire start-up process from ambient to high operating temperature. Validation of key results suggests a close resemblance between the model and an actual system. Therefore, the proposed model is expected to exceed the limitations of the existing static model analysis method.