Addison Porter Jones (September 15, 1822 – May 5, 1910) was an American politician from New York.
He was Supervisor of the Town of Catskill in 1856, 1860 and 1861; and Sheriff of Greene County from 1862 to 1864.
He was a presidential elector in 1876, voting for Samuel J. Tilden and Thomas A. Hendricks.
His grandson, Addison Porter Jones II was named after him.
He married Annette Whittaker and was the president of the Catskill Savings Bank.