Carbon neutrality in the aviation field is the essential development direction, which required multi-field and multi-disciplinary knowledge. One of the most efficient methods is developing low-carbon propulsion systems. Ducted fan engines integrated with high temperature fuel cells are proposed. Fuel cells are used to provide power to the compressed parts. Simultaneously, it works at high pressure conditions and has a high power density. The propulsion power is produced by the expansion of the high temperature fuel cell exhaust in the internal duct and the cold air in the external duct. So, not only can the novel engine be operated at the maximum efficiency mode when the total fuel is injected into the fuel cell system, but also the maximum thrust mode can be achieved by increasing air mass flow and inlet temperature of the nozzles. Detailed mathematical models are built to evaluate its capacity and conclusions are as follows: (1) the optimization direction of the weight of the engine is opposite to that of the specific impulse. (2) Under the same thrust standards, the compressor ratio and combustion temperature for the engine are respectively extremely lower than that of the original engine, but the specific fuel consumption of the former still can decrease by 46% accompanied by the weight rise by 160%. (3) Altitude characteristic study shows that the engine performs well at high altitudes. The thermal efficiency and propulsion efficiency both rise with increasing altitude.