Let A, B, G be groups. G is called a Schreier extensions of A by B if A is a normal subgroup of G and G/A is isomorphic to B. In this paper, by using the Grobner-Shirshov bases, we give characterizations of the Schreier extensions of groups when the group B is presented by generators and relations. An algorithm to find the conditions of a group G to be a Schreier extension of A by B is obtained. By introducing a special well order, we obtain the structure of the Schreier extension by an HNN group.