Marston is a city in New Madrid County, Missouri, United States. The population was 503 at the 2010 census. A post office called Marston …Marston is a city in New Madrid County, Missouri, United States. The population was 503 at the 2010 census. A post office called Marston has been in operation since 1898. The community was named after the mother's maiden name of an early settler. Marston was incorporated in 1905.