Shaw was born at Bellinborough, Lincolnshire, England in 1776 or 1777 and received his first training as a sign painter's apprentice. In 1802 he exhibited at the Royal Academy for the first time. The artist came to the United States around 1817 and travelled through Virginia and several other southern states to execute sketches and take subscription orders for a series of engravings of these southern views. Shaw settled in Philadelphia in 1819 or 1820 and was helpful in the formation of the Artist's Fund Society in the early 1840s. He exhibited frequently at the American Art Union, National Academy of Design, and the Pennsylvania Academy.