Anderson's training as a shipwright stood him in good stead when he became an artist specializing in maritime art based on the Dutch 17th century Masters. He first exhibited at the Royal Academy in 1780 and continued to exhibit annually until 1811. He then exhibited intermittently until 1834. His best work was executed in the years 1790–1810, during the French Revolutionary and Napoleonic Wars, at which time the demand for naval paintings was high. His painting was not restricted to marine subjects.