Superconducting Radio-Frequency (SRF) cavities are used to accelerate particles in particle accelerators. In this application, the cavity is made of niobium (Nb) material and the inner surface of cavity should be polished so as to obtain the high performance of particle accelerator. The Electro-Polishing (EP) process is one of the best methods to polish the inner-surface of Nb cavity where the electrolyte is the mixture of sulfuric and hydrofluoric acids. However, this EP electrolyte is very dangerous in the operation and thus the operators need rigorous protection. Furthermore, all parts of instrument for the EP process must be made of high density polyethylene or fluorocarbon resin because the corrosion of metal occurs by hydrofluoric acid. These are the reasons why the cost of EP process becomes very expensive. In addition, the EP process produces sulfur compound on the Nb surface as a by-product. This sulfur compound can be the sources of field-emission on the inner surface of cavity and degrades the accelerating performance. In this article, we report a novel EP method using periodic reverse current and sodium hydroxide solution. The reaction produces no sulfur content and the instrument is less expensive because it is made of usual plastic material. As the result of experiments with Nb-coupon samples, we found that the surface roughness is equivalent to the conventional EP method. And some experiments with a Nb single-cell cavity will be reported.