Groesbeck is a city in and the county seat of Limestone County, Texas, United States. Its population was 3,631 at the 2020 census. The com…Groesbeck is a city in and the county seat of Limestone County, Texas, United States. Its population was 3,631 at the 2020 census. The community is named after a railroad employee. The city of Groesbeck was dedicated as a township by Houston and Texas Central Railroad in 1869. It was named for Abram Groesbeeck, a railroad director of the Houston & Texas Central Railroad Company. The difference in spelling between the person and town is a result of the post office directives for simpler spelling. Development of its city government began in 1871. Groesbeck became the county seat of Limestone County in 1873, and is home to the "Million Dollar Courthouse". Fort Parker State Park, located north of Groesbeck, is preserved to tell the story of Cynthia Ann Parker, who was captured by Comanches, and became the mother of Quanah Parker, the last Comanche chief. The last legal execution in Limestone County occurred on April 12, 1895, when Richard Burleson, who had been convicted of murdering James Garrett McKinnon, was hanged in front of the courthouse in Groesbeck.