Born in Edgefield District, South Carolina, Landrum pursued classical studies and graduated from South Carolina College (now the University of South Carolina) at Columbia in 1842. He taught school for several years as he studied law. He was admitted to the bar in 1844 and commenced the practice of law in Shreveport, Louisiana.
He served as mayor of Shreveport in 1848 and 1849.
Landrum was elected as a Democrat to the Thirty-sixth Congress (March 4, 1859 - March 3, 1861). He was not a candidate for renomination in 1860 to the Thirty-seventh Congress.
He continued the practice of his profession until his death in Shreveport on October 18, 1861.
He was interred in Oakland Cemetery.