The exploitation of heavy oil reservoirs calls for the implementation of thermal recovery techniques. To provide the heat source for oil recovery energy system, NCLFR-Oil, a Natural Circulation Lead-bismuth Fast Reactor was designed for heavy oil extraction, with a designed power of 40 MW and a lifetime of at least 15 years. In order to achieve the designed object for a reactor core that is durable, compact, transportable, and exhibits strong passive and active safety features, the selection of core materials such as fuel and absorber, evaluation of reactivity control system and corresponding neutronic performance have been optimized by iterative design in this paper with the reference of many small modular reactors. The depletion calculation confirms that the designed reactor can operate for 19 years without refueling. Neutronic performance were analyzed for multiplication factor within lifetime, isotopes conversion, neutron energy spectrum, radial and axial power distributions, nuclear fission reaction rates, reactivity feedback coefficients, and control rod worth with shutdown margins. The core analysis shows that the reactor has good power and safety characteristics, which can fully meet the energy demand of heavy oil exploitation.