According to data in FamilySearch.org, His parents were
Henry Smith 1729-1792
Catharine Amelia "Amy" Hampton 1726-1808
They were married in 1747 in Augusta, Colony of Virginia, British Colonial America and had 18 children
Abraham 1747-1806, John 1748-1834, Sarah 1749-?, William 1750-1781, Gideon 1752-1783, Elizabeth 1754-1845, Daniel 1756-1779, Henry Jr 1759-1840, Jonathan 1862-1829, William 1764-?, Sarah 1766-1806, David 1771-1806, Britian 1775-1862, Cynthia ?-?, James ?-?, Nathaniel ?-?, Nelly ?-?, Rachel ?-?. Some of these children have the same names so I would be suspicious that these are all their children.
Hope this helps.