James Sevier Conway was born in Greene County, Tennessee. Conway was educated by private tutors and attended public schools.
In 1820 he moved to Arkansas where he worked as a surveyor. He formed a surveying business with two of his brothers. Conway's company took over the land that would later become the city of Little Rock, Arkansas and he is known as the founder of that city. Conway purchased a large cotton plantation in the town of Walnut Hill in Lafayette County, Arkansas.
In 1832 Conway became the surveyor-general of the Arkansas Territory and served in that position until 1836.
Conway became the first elected Governor of Arkansas when it became a state in 1836. Conway focused his administration on schools and roads. He established a state militiary to patrol the western frontier and worked to have a federal arsenal established at Little Rock, Arkansas. He worked to get funding for a state penitentiary. He pushed for the establishment of a state library and university but was unsuccessful.
Conway left office in 1840 and returned to his plantation. He continued to be active in public affairs.
James S. Conway is buried at the Conway Cemetery Historic State Park near Bradley, Arkansas.
James Sevier Conway was the brother of Arkansas Governor Elias Nelson Conway, brother of Congressman Henry Wharton Conway, first cousin of Senator Ambrose Hundley Sevier and Governor Henry Massey Rector. He was third cousin of Confederate General James Lawson Kemper.