The son of a fancy goods merchant, Grassi was sent to the Vienna Academy in 1768. Attractive and talented, he soon obtained access to the Viennese court as a portraitist and in 1791 was received into the Vienna Academy as a portrait painter. He was called to Warsaw in 1790, where he worked for the King, Stanislaus August II, eventually becoming the leading portraitist at the Polish court. Allied to the patriot party he portrayed many of its heroes whose portraits he invested with an elegance reminiscent of English eighteenth-century portraiture. He was back in Vienna in 1795-6, and was named professor at the Dresden Academy in 1800. His success as a painter allowed him to build a fine villa in Dresden. He was named Director of the Saxon School in Rome in 1817. Grassi spent his last years in Dresden, increasingly infirm and largely ignored.