The artist was born in Chichester to William Smith, a tradesman. Both of his brothers, John (c. 1717-64) and William (1707-64), were also artists. Charles, 2nd Duke of Richmond and Lennox (1701-1750) was a major patron of the brothers and encouraged their interest in landscape painting. In 1760, George won the first landscape premium offered by the Society for the Encouragement of the Arts, Manufactures and Commerce. The brothers' reputation was spread through engravings by Woollett, William Elliot, James Peake and Francois Vivares, many of which were exported to France.