Cosmopolis is a city in Grays Harbor County, Washington, United States. The population was 1,638 at the 2020 census. According to the Uniteā¦Cosmopolis is a city in Grays Harbor County, Washington, United States. The population was 1,638 at the 2020 census. According to the United States Census Bureau, Cosmopolis has a total area of 1.52 square miles, of which, 1.33 square miles is land and 0.19 square miles is water.