Sponsored Topics. Bevier is a city in Macon County, Missouri, United States. The population was 718 at the 2010 census. Bevier is located at 39°44′57″N 92°33′50″W / 39.74917°N 92.56389°W / 39.74917; -92.56389 (39.749126, -92.563902). According to the United States Census Bureau, the city has a total area of 0.9 square miles (2.2 km²), all of it land.