The FIMS(Far-ultraviolet IMaging Spectrograph), the main payload onboard the first Korean Science Technology SATellite, STSAT-1, has performed various astronomical observations, including the Cygnus Loop, Vela supernova remnants, LMC(Large Magellanic Cloud), since its launch on September 2003. It has been found that the attitude information provided by spacecraft bus system has the errors of more than about 10-15 arcmins due to the time offset problem and errors in attitude knowledge. We develop an algorithm for correction of position errors in FIMS data. The aspect for the FIMS data is determined by comparing the positions of observed bright stars with the Tycho-II and TD-1 catalogs. The position errors of the bright stars along the scanning ( γ) and spatial (δ ) directions were considered as functions of δ, ignoring errors in position angle. The corrected positions of the bright stars coincided very well to their Tycho-II and TD-I positions. The correction algorithm is essential for the FIMS data analysis, and is being used for the FIMS data analysis.