A liquid-fuel heat-pipe reactor (LFHPR) is a novel fast heterogeneous reactor developed by Harbin Engineering University, China, on the basis of liquid-fuel reactor designs and the heat-pipe reactor concept. In the concept, the reactor abandons the graphite moderator and keeps neither fuel tubes arranged in the graphite nor fuel rings around the heat pipe. Instead, the reactor applies molten salt fuels, molten metallic eutectic fuels, or other fuels in liquid form. The heat generated in the reactor is removed by the heat pipes driven by liquid metals. With this change, an LFHPR is much more flexible in design and application and able to achieve several advanced features compared with conventional heat-pipe reactors. In this paper, we describe the general reactor design of an LFHPR, discuss its potential advantages, and give a preliminary verification of the neutron physical feasibility for the reference case, which uses molten salt as the fuel, by using both Monte Carlo and deterministic methods. Results show that the LFHPR yields a hard neutron spectrum that brings a very good neutron economy and is a promising application for breeding. From our approach, we conclude that the proposed LFHPR has a very high power density and high negative temperature feedback coefficient.