  Proximity induced superconducting states in the surface of magnetically doped
topological insulators can host chiral Majorana modes. We consider a Josephson
junction in that system with changing the chemical potential, which drives a
topological phase transition in the induced superconducting states as well as a
metal-insulator transition in the surface states. The local density of states
and the Josephson current are analytically calculated by McMillan's Green's
function method in terms of the Andreev reflection coefficient. We show that
although the magnitude of the Josephson current is greatly enhanced when the
surface state changes from insulating to metallic, its temperature dependence
drastically changes at the topological phase transition point, reflecting the
appearance of the chiral Majorana modes
