Hugh Gibson Brown was born on December 29, 1835, in Luzerne County, Pennsylvania, to Hugh Brown and Mary Gibson. He eventually moved to Keosauqua, Iowa, and the 1860 census listed him as a student. On December 1, 1861, he received a commission as a 2nd lieutenant in Company E of the 15th Iowa Infantry. The regiment took part in the Battle of Shiloh, the siege of Corinth, and the Vicksburg campaign. He was promoted to 1st lieutenant on July 9, 1862. Then, on August 28, 1863, he was promoted to captain and became aide-de-camp to General Edward Ord. He was breveted a major on September 29, 1864, and then breveted a lieutenant colonel on March 31, 1865. He mustered out on July 10, 1866.
Later that year, Brown received a commission as a 2nd lieutenant in the United States Regular Army. He spent the next three decades in the 36th U.S. Infantry and the 12th U.S. Infantry, eventually becoming a major. He retired in May 1899. He returned to Keosauqua after leaving the army, and he died there of heart disease on November 30, 1901.