A core design of small modular liquid-metal fast reactor (SMLFR) cooled by lead-bismuth eutectic (LBE) was developed for power reactors. The main design constraint on this reactor is a size constraint: The core needs to be small enough so that (1) it can be transported in a spent nuclear fuel (SNF) cask to meet the electricity demands in remote areas and off-grid locations or so that (2) it can be used as a power source on board of nuclear icebreaker ships. To satisfy this design requirement, the active core of the reactor is 1 m in height and 1.45 m in diameter. The reactor is fueled with natural and 13.86% low-enriched uranium nitride (UN), as determined through an optimization study. The reactor was designed to achieve a thermal power of 37.5 MW with an assumption of 40% thermal efficiency by employing an advanced energy conversion system based on supercritical carbon dioxide (S-CO2) as working fluid, in which the Brayton cycle can achieve higher conversion efficiencies and lower costs compared to the Rankine cycle. The outer region of the core with low-enriched uranium (LEU) performs the function of core ignition. The center region plays the role of a breeding blanket to increase the core lifetime for long cycle operation. The core working fluid inlet and outlet temperatures are 300 degrees C and 422 degrees C, respectively. The primary coolant circulation is driven by an electromagnetic pump. Core performance characteristics were analyzed for isotopic inventory, criticality, radial and axial power profiles, shutdown margins (SDM), reactivity feedback coefficients, and integral reactivity parameters of the quasi-static reactivity balance. It is confirmed through depletion calculations with the fast reactor analysis code system Argonne Reactor Computation (ARC) that the designed reactor can be operated for 30 years without refueling. Preliminary thermal-hydraulic analysis at normal operation is also performed and confirms that the fuel and cladding temperatures are within normal operation range. The safety analysis performed with the ARC code system and the UNIST Monte Carlo code MCS shows that the conceptual core is favorable in terms of self-controllability, which is the first step towards inherent safety.