In this paper, we define the Grobner-Shirshov basis for a dialgebra. The Composition-Diamond lemma for dialgebras is given then. As results, we give Grobner-Shirshov bases for the universal enveloping algebra of a Leibniz algebra, the bar extension o
f a dialgebra, the free product of two dialgebras, and Clifford dialgebra. We obtain some normal forms for algebras mentioned the above.
