The cut polytope of a graph is an important object in several fields, such as functional analysis, combinatorial optimization, and probability. For example, Sturmfels and Sullivant showed that the toric ideals of cut polytopes are useful in algebraic statistics. In the theory of lattice polytopes, the h^*-polynomial is an important invariant. However, except for trees, there are no classes of graphs for which the h^*-polynomial of their cut polytope is explicitly specified. In the present paper, we determine the h^*-polynomial of the cut polytope of the complete bipartite graph K_2,m using the theory of Gröbner bases of toric ideals.