A neutronics study of a supercritical CO2-cooled fast reactor core for nuclear propulsion has been performed in this work. The thermal power of the reactor core is 30 MWth and a ceramic UO2 fuel can be used to achieve a 20-year lifetime without refueling. In order to make a compact core with inherent safety features, the drum-type reactivity control system and folding-type shutdown system are adopted. In addition, we suggest a cold shutdown system using gadolinium as a spectral shift absorber (SSA) against flooding. Although there is a penalty of U-235 enrichment for the core embedded with the cold shutdown system, it effectively mitigates the increment of reactivity at the flooding of seawater. In this study, the neutronics analyses have been performed by using the continuous energy Monte Carlo Serpent 2 code with the evaluated nuclear data file ENDF/B-VII.1 Library. The supercritical CO2-cooled fast reactor core is characterized in view of important safety parameters such as the reactivity worth of reactivity control systems, fuel temperature coefficient (FTC), coolant temperature coefficient (CTC), and coolant temperature-density coefficient (CTDC). We can say that the suggested core has inherent safety features and enough flexibility for load-following operation.