Groesbeck is a city in and the county seat of Limestone County, Texas, United States. Located along Texas State Highway 14 and Texas Sta…Groesbeck is a city in and the county seat of Limestone County, Texas, United States. Located along Texas State Highway 14 and Texas State Highway 164, it sits in the northern part of the Texas Triangle. Its population was 3,631 at the 2020 census.