 Vivian was the son of John Vivian (1750–1826), of Truro, Cornwall, and his wife Betsey, daughter of the Reverend Richard Cranch, and the brother of Hussey Vivian, 1st Baron Vivian.He owned copper mining, copper smelting and trading businesses in Swansea (Vivian & Sons), Liverpool, Birmingham and London.Between 1832 and 1855 he sat as Member of Parliament for Swansea District.