Francis Cotes (20 May 1726-16 July 1770) was an English painter, one of the pioneers of English pastel painting, and a founder member of the Royal Academy in 1768.

Born in London, the eldest son of Robert Cotes, an apothecary (Francis's younger brother Samuel Cotes (1734–1818) also became an artist, specialising in miniatures), and trained with portrait painter George Knapton (1698-1778) before setting up his own business in his father's business premises in London's Cork Street – learning, incidentally, much about chemistry to inform his making of pastels.

An admirer of the pastel drawings of Rosalba Carriera , Cotes concentrated on works in pastel and crayon (some of which became well-known as engravings), but later added oil painting to his repertoire. In 1763, he bought a large house (later occupied by George Romney) in Cavendish Square.

One of the most fashionable portrait painters of his day, Cotes helped found the Society of Artists and became its director in 1765. At the peak of his powers, Cotes was invited to become one of the first members of the Royal Academy, but died just two years later, aged 44, in Richmond upon Thames.

He also taught pastel skills to John Russell, and his skills were described in Russell's book The Elements of Painting with Crayon.