Robert Salmon was christened on 5 November 1775 in Whitehaven, England. Nothing is known about his training, though it is assumed that he probably went to London in the 1790s, where the Royal Academy showed a few of his works from 1802 onwards. He later lived in Liverpool and from 1811 in Greenock. From this moment onwards Salmon preferred to depict the marine landscapes that surrounded him, which denote his knowledge of the Dutch painters of seascapes, the Italian painters of vedute and the work of Claude Lorrain.

Salmon arrived in Boston in 1828. Although solitary by nature, he soon became one of the most prominent seascape painters. During the following years he divided his time between painting and working in the lithographic studio of William S. Pendleton, where he coincided with Fitz Hugh Lane. This contact between the two painters was of great importance to Lane and became evident in his marine views.

In 1842 Salmon left Boston, probably to return to England. His last documented work was executed in 1845.