He studied Biblical exegesis and oriental languages at the University of Strassburg under Édouard Reuss, and, after holding various teaching posts, was made instructor in French and Hebrew at the Landesschule of Meissen, receiving in 1852 the title of professor.
In his principal work, Die geschichtlichen Bücher des Alten Testaments (1866) he sought to show that the priestly legislation of Exodus, Leviticus and Numbers is of later origin than the book of Deuteronomy.
He still, however, held the accepted view, that the Elohistic narratives formed part of the Grundschrift and therefore belonged to the oldest portions of the Pentateuch.
The idea had already been expressed by Reuss, but since Graf was the first to introduce it into Germany, the theory, as developed by Julius Wellhausen, has been called the Graf-Wellhausen hypothesis.
See T. K. Cheyne, Founders of Old Testament Criticism (1893); and Otto Pfleiderer's book translated into English by J. F. Smith as Development of Theology (1890).