Analysis on the perturbation expansion for the single orbital Anderson model is extended to an orbital-degenerate case. The self-energy and the vertex part are analyzed. There appear two independent parameters in the vertex part at zero frequencies due to the symmetry of the Hamiltonian. A relation is found between the specific heat and susceptibilities including the orbital one due to the impurity at the low temperature limit. Resistivity is discussed in the case of the half-filled localized electrons.