A multi-channel $H_α$ spectroscopic diagnostic system was developed on KAIST-Tokamak to be utilized as specifing the plasma position in the start-up phase of ohmic discharges. The system consists of collimators, interference filters with 10nm bandwidth to selectively obtain $H_α$ radiation, optical fibers for light transport, and a number of photomultiplier tubes for light detection. The diagnostic setup was installed at the outboard-side of the tokamak and arranged vertically to measure the $H_α$ intensities in several vertical positions. Since the measured intensity is line-integrated along the line of sight, an Abel inversion program was developed using the slice and stack method. The vertical (similar to minor radial) profile was obtained by the invertsion program and the center position of the intensity was obtained at several time steps in the start-up phase of KAIST-Tokamak ohmic discharges. The center position of the intensity is an indirect indication of the plasma center. Comparision of the center position obtained in this way with the magnetics data show reasonable agreement. This suggests that the multi-channel $H_α$ diagnostic may be an excellent candidate to determine the plasma position which can be used especially for plasma position control in the tokamak start-up phase.