Aircraft nuclear propulsion system can significantly enhance the endurance, but its large size and weight become disadvantages against the conventional fossil fuel propulsion system. In this paper, a novel nuclear power and fossil fuel hybrid propulsion system, which combines the lithium-cooled fast reactor and the kerosene-fueled turbine engine, is proposed to meet the power requirements of different flight segments. Performance assessment and comparison among different hybrid configurations is performed. Results indicate that the configuration combining the nuclear power module with a high bypass ratio turbofan engine is the most promising for aircraft. The primary optimization shows that there is a trade-off between the weight of the nuclear power module and the specific thrust, and the optimal weight of nuclear power module is 3942 kg, with the specific thrust of 195.8 N·kg-1·s-1. The aircraft equipped with the hybrid propulsion system operates at the maximum altitude of approximately 18.2 km and reaches a maximum Mach number of 0.71, allowing for sustained flight for several months in cruise segment. The turbofan engine, nuclear reactor, ancillary systems, shield, and heat exchanger account for 11%, 23%, 11%, 17% and 1% of the fuel mass of the original unmodified aircraft.