Phelps County is a county located in the U.S. state of Nebraska. As of the 2010 census, the population was 9,188. Its county seat is Holdrege. The county was formed in 1873 and named after William Phelps, an early settler in this area.In the Nebraska license plate system, Phelps County is represented by the prefix 37 (it had the thirty-seventh-largest number of vehicles registered in the county when the license plate system was established in 1922).