Parrish was engaged in mercantile pursuits until he was 30, when he applied himself to art, studying for a year with a local teacher. In 1878 he first exhibited at the Pennsylvania Academy in Philadelphia, and in 1879 at the National Academy in New York City. He soon turned his attention also to etching, and in December 1879, produced his first plate. After that he applied himself to both branches of art, exhibiting in New York City, Boston, Philadelphia, London, Liverpool, Paris, Munich, Dresden, and Vienna. He was a member of the New York Etching Club and the Society of Painter-Etchers of London. From 1884 to 1886, he traveled in Europe.
His etchings include Northern Moorland and Low Tide — Bay of Fundy (1882); Coast of New Brunswick, Winter Evening — Windsor, Nova Scotia, and Bethlehem (1884); London Bridge and On the Thames (1886); and A Gloucestar Wharf (1887). Among his paintings are November (1880); In Winter Quarters (1884); Low Tide — Evening (1885); On the Rance, Brittany (1886); and The Road to Perry's Peak. He also made etchings of several of his pictures.