With a diamond fractal lattice, the Ising model was exactly solved by parameter_ transformation technique. The rigorous partition function, free energy and corre lation functions were obtained for zero as well as non_zero field. In particular , an equation of cumulant pair correlation function and its analytical asymptoti c expression was derived in the zero field. The result indicated that the corre lation behaviors of the Ising model on a diamond fractal lattices are similar to the two_dimensional transitionally invariant lattices.