We analyze a Wannier-Mott exciton in which the electron is constrained to move in a quantum ring and the hole moves in another concentric quantum rings. We expand the electron-hole interaction potential in terms of multipoles by assuming that both the electron and hole experience transverse harmonic confinements in the ρ and z directions, both being in their respective transverse groundstates. For the resulting φ-dependent Schrodinger equation we calculate the lowest exciton eigenenergies and eigenfunctions.