The formula of one-electron theory for the circulating currents in normal metal hollow cylinders, threaded by magnetic flux of Aharonov-Bohm type, is proven. The form of it is independent of either the shape of cylinder or the properties of carriers (charge and mass). The exact solutions of energyeigen values and wave-functions have been obtained for the perfect lattice case. We have also studied the periodicity of currents varying with the magnetic flux and the increasing tendency of current amplitudes with the height and thickness of cylinder wall. A number of new results have obtained in this work.