There are 5 US Post Offices in Grant County serving a total of 16,528 residents equating to 3,306 residents per post office. It's estimated that approximately 26,381 packages are handled across the 5 county post offices annually. Grant County is a county in the U.S. state of Arkansas. Its population was 17,853 at the 2010 United States Census. The county seat is Sheridan. Grant County is included in the Little Rock\u2013North Little Rock\u2013Conway, AR Metropolitan Statistical Area."