Joseph Addison Woodward (April 11, 1806 – August 3, 1885) was an American politician who served as a U.S. Representative from South Carolina.

Born in Winnsboro, South Carolina, Woodward received an academic training and was graduated from the University of South Carolina at Columbia.

Woodward served as member of the State house of representatives from 1834 to 1835 from 1840 to 1841.

He declined to be a candidate for reelection in 1852 to the Thirty-third Congress.

He relocated to Alabama and resumed his legal career after leaving Congress.