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The cut polytope of a graph is an important object in several fields, such asfunctional analysis, combinatorial optimization, and probability. For example,Sturmfels and Sullivant showed that the toric ideals of cut polytopes areuseful in algebraic statistics. In the theory of lattice polytopes, the$h^{*}$-polynomial is one of the most important invariants. The necessary andsufficient condition in terms of graphs that the $h^{*}$-polynomial of a cutpolytope is palindromic is known. However, except for trees, there are noclasses of graphs for which the $h^{*}$-polynomial of their cut polytope isexplicitly specified. In the present paper, we determine the $h^{*}$-polynomialof the cut polytope of complete bipartite graph $K_{2,m}$ using the theory ofGr\"{o}bner bases of toric ideals.

The $h^{*}$-polynomial of the cut polytope of $K_{2,m}$ in the lattice spanned by its vertices