Conway is a city in Laclede County, Missouri, United States. The population was 729 at the 2020 census. Conway is located 15 miles (24 km) southwest of Lebanon. Conway was platted in 1869, and named after a local merchant. A post office has been in operation at Conway since 1871. According to the United States Census Bureau, the city has a total area of 1.83 square miles (4.74 km²), of which 1.82 square miles (4.71 km²) is land and 0.01 square miles (0.03 km²) is water. As of the census of 2020, there were 729 people, 359 households, and 279 families residing in the city.