In this paper,we find Haal-Shirshov type bases for free pre-Lie algebras.We show that Segal’s basis of a free pre-Lie algebra is a type of these bases.We give a nonassociative Gr(o)bner-Shirshov basis S for a free pre-Lie algebra such that Irr(S) is a monomial basis (called normal words) of a free pre-Lie algebra,where Irr(S) is the set of all nonassociative words,not containing maximal nonassociative words of polynomials from S.We establish the Composition-Diamond lemma for free pre-Lie algebras over the basis of normal words and the degree breadth lexicographic ordering.