We have used the near-infrared $JHK_S$ photometric data of resolved stars in a nearby dwarf elliptical galaxy NGC 205 to determine the magnitudes of the red giant branch tip (TRGB). By applying Savitzky-Golay filter to the observed luminosity functions (LFs) in each band, we derived the second derivatives of the LFs so as to determine the magnitudes of the TRGB. Absolute magnitudes of the TRGB in $JHK_S$ bands were measured from the Yonsei-Yale isochrones. By comparing the determined apparent magnitudes and the theoretical absolute magnitudes of the TRGB, we estimated the distance moduli of NGC 205 to be (m - M) = $24.10{pm}0.08$, $24.08{pm}0.12$ and $24.14{pm}0.14$ in J, H, and $K_S$ bands, respectively.