Blevins was the son of John and Margaret Oldham Connally Blevins of Alabama. He moved to East Texas and married Tassie Belle Lawdermilk there. Inspired by outcroppings of iron ore in Cherokee County, Texas, he raised capital to purchase 20,000 acres of land in 1887 and construct two blast furnaces, along with the manufacturing and social requirements for a planned boomtown. Innumerable misfortunes, chiefly the Panic of 1893, beset the project. Blevins' attempt to restart the development of New Birmingham in 1907 was stymied by another financial panic that year.
Blevins relocated to Shreveport, Louisiana in September 1912 and there organized the North Louisiana Interurban and Electric Railway Company, serving as its president. He planned to extend interurban lines to Monroe, Louisiana and Marshall, Texas.
Blevins died from heart failure in 1915 and was buried at Shreveport's Oakland Cemetery.
Blevins and his wife had one daughter, Olive Marguerite, who later married Zack Miller, the youngest son of George Miller, founder of the famed 101 Ranch in Ponca City, Oklahoma. Zack and his brothers created the "101 Ranch Wild West Show" which toured the country and internationally until falling into bankruptcy in the early 1930s.
- "Maj. A. B. Blevins died very suddenly." (March 5, 1915) Monroe News-Star
- Anderson B. Blevins at Findagrave.com