Small modular reactors with power below 300 MW have the advantages of small specific mass, long lifetime, and flexible power supply, and they are suitable for providing power support for small and medium-sized towns with small populations and remote areas without grid coverage. In this paper, a small modular S-CO2-cooled molten salt reactor is proposed, and the design of a 10 MW small modular chlorine salt fast reactor (sm-MCFR) with 20 years of operation without refueling is presented. The neutron feasibility of the S-CO2-cooled small modular chlorine fast reactor is analyzed in terms of neutron energy spectrum, reactivity control, temperature reactivity coefficient, and power distribution. A distinctive feature of the sm-MCFR is the use of chlorine salts with high heavy metal solubility and a hard energy spectrum, allowing the core size to be minimized while maintaining the maximum lifetime. The designed core is about 2.44 m in diameter and 2.24 m in height. Meanwhile, the sm-MCFR uses control drum control as the control system, which can effectively achieve reactivity control without increasing the reactor size. The final optimized sm-MCFR has a negative temperature reactivity coefficient, which is necessary to ensure the safe operation of the reactor.