Grant County is a county located in the U.S. state of Minnesota. As of 2000, the population is 6,289. Its county seat is Elbow Lake. According to the U.S. Census Bureau, the county has a total area of 575 square miles (1,490 kmē), of which, 546 square miles (1,415 kmē) of it is land and 29 square miles (75 kmē) of it (5.00%) is water. As of the census of 2000, there were 6,289 people, 2,534 households, and 1,740 families residing in the county. The population density was 12 people per square mile (4/kmē). There were 3,098 housing units at an average density of 6 per square mile (2/kmē).