Landrum is a city in Spartanburg County, South Carolina, United States. The population was 2,376 at the 2010 census. Landrum was foundeā¦Landrum is a city in Spartanburg County, South Carolina, United States. The population was 2,376 at the 2010 census. Landrum was founded in 1880 and incorporated in 1912. It is located just west of Interstate 26 between Spartanburg and Asheville, North Carolina.