Abstract: Various graph theoretic properties of the commuting graph \Delta \left( GB_n \right) of a generalized Brandt semigroup, including diameter, girth, matching number, independent number, and clique number are investigated. The conditions under which the commuting graph of a generalized Brandt semigroup is Eulerian, Hamiltonian, planar and perfect are given, respectively. The structure of the commuting graph of a generalized Brandt semigroup is explored.