In the spirit of the thin-layer quantization scheme, we give the effective Hamiltonian describing the noninteracting electrons confined to an annular corrugated surface, and find that the geometrically induced potential is considerably influenced by corrugations. By using a numerical calculation, we investigate the eigenenergies and the corresponding eigenstates, and find that the transition energies can be sufficiently improved by adding corrugations. Particularly, the transition energy between the adjacent eigenstates corresponds to energy level differences based on the wavefunction of annular wire, and the number of the energy levels is equal to the number of corrugations. Furthermore, the larger magnitude of corrugations is capable of increasing the number of bound states. In addition, the distribution of ground state probability density is reconstructed by the corrugations, and the energy shift is generated.