Alexander Barrow I (March 27, 1801 – December 29, 1846) was a lawyer and United States Senator from Louisiana. He was a member of the Whig Party. He was the half-brother of Washington Barrow, sharing the same father. Born near Nashville, Tennessee, to Willie Barrow and his first wife Jane Green, Barrow attended the United States Military Academy in West Point, New York, from 1816 to 1818. Then he studied law and was admitted to the bar, in 1822, commencing practice in Nashville. Soon afterward he relocated to Feliciana Parish, Louisiana, where he continued to practice law. Later he abandoned his legal career to become a planter. Eventually, Alexander Barrow became involved in politics and was elected to the Louisiana House of Representatives, where he served for several years. In 1840 Barrow was elected a Whig to the United States Senate, serving from 1841 until his death. There he was Chairman of the Committee on Public Buildings and Grounds during the 27th Congress and of the Committee on the Militia during the 27th and 28th Congresses. Senator Barrow died in Baltimore, Maryland, on December 29, 1846. His remains were interred in the family cemetery on Afton Villa plantation, near Bayou Sara, Louisiana. Alexander and Mary Ann Barrow had three children, Alexander II, Willie Micajah, and Jane.