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