Parma is a city in Cuyahoga County, Ohio, United States. It is a suburb located south of Cleveland. As of the 2020 census, its population wa…Parma is a city in Cuyahoga County, Ohio, United States. It is a suburb located south of Cleveland. As of the 2020 census, its population was 81,146. Parma is the seventh-most populous city in Ohio, the largest suburb in the state, and the second-largest city in Cuyahoga County.