Mound City is a city in and the county seat of Linn County, Kansas, United States. As of the 2020 census, the population of the city was 647. Mo…Mound City is a city in and the county seat of Linn County, Kansas, United States. As of the 2020 census, the population of the city was 647. Mound City was founded in 1855. It was named from Sugar Mound nearby, a hill covered with sugar maple trees.