Garfield County is a county located in the U.S. state of Nebraska. As of the 2010 census, the population was 2,049. Its county seat is Burwell. The county was organized in 1884 and named for James A. Garfield, 20th President of the United States.In the Nebraska license plate system, Garfield County is represented by the prefix 83 (it had the eighty-third-largest number of vehicles registered in the county when the license plate system was established in 1922).