Born in Manchester, England, Burrows immigrated to the United States with his parents, who settled in Quincy, Illinois. He attended the common schools at Quincy, Illinois, and Keokuk, Iowa. He engaged in mercantile pursuits and later in agricultural pursuits. He moved to Cainsville, Missouri, in 1862. He was ordained as a minister in Cainsville in 1867. He served as member of the State house of representatives in 1870-1874 and 1878-1880.
Burrows was elected as a Greenback to the Forty-seventh Congress (March 4, 1881 - March 3, 1883). He was an unsuccessful candidate for reelection in 1882 to the Forty-eighth Congress. He resumed ministerial duties and also engaged in agricultural pursuits. He died in Cainsville, Missouri, April 28, 1914. He was interred in Oak Lawn Cemetery, near Cainsville.