A novel concept of solid oxide fuel cell (SOFC)-based hybrid power generation—an SOFC–engine hybrid—is introduced, and proof-of-concept test results for a 5-kW-class system are presented. The SOFC–engine hybrid system is a combination of an SOFC and internal combustion engine, consisting of an SOFC stack, a reformer, an air blower, a fuel supply system, a water pump, an air preheating exchanger, a steam generator, and an internal combustion engine. To prove the feasibility of the proposed hybrid system concept, a 5-kW-class small-scale demonstration system was integrated with the proposed system, and tests were performed under various experimental conditions with pure hydrogen fuel and reformed methane gas. In the hydrogen-based test, the SOFC and engine generated 4.4 kW and 731 W, respectively, at 70% fuel utilization. This indicates that the engine improved the efficiency by 7.9% compared with fuel-cell-only operation (47.8%). In the reformed gas test, the demonstration was conducted for more than 200 h. At a lower fuel utilization of 50.6%, the SOFC and engine generated 3.3 kW and 1168 W, respectively; the engine accounted for 26.0% of the total net power production. As the fuel utilization increased, the power share of the engine decreased; the engine accounted for 17.3%, 13.1%, and 7.6% of the total net power at fuel utilizations of 61.2%, 65.4%, and 70.1%, respectively. Based on the results, it can be concluded that at 70.1% fuel utilization, the efficiency improved by 5.3% because of the additional power from the engine. Through a series of tests, it was observed that at a fuel utilization of more than 65%, the total power production and sum of the SOFC power and engine power maintained similar values because the engine compensated for the power decrease in the SOFC stack.