We investigated the distribution of resolved asymptotic giant branch (AGB) stars over a much larger area than covered by previous near-infrared studies in the nearby dwarf elliptical galaxy NGC 205. Using data obtained with the WIRCam near-infrared imager of the CFHT, we selected the AGB stars in the JHKs color - magnitude diagrams, and separated the C stars from M-giant stars in the JHKs color - color diagram. We identified 1,550 C stars in NGC 205 with a mean absolute magnitude of =-7.49+/-0.54, and colors of =1.81+/-0.41 and =0.76+/-0.24. The ratio of C stars to M-giant stars was estimated to be 0.15+/-0.01 in NGC 205, and the local C/M ratios for the southern region are somewhat lower than those for the northern region. The (J-K) color distributions of AGB stars contain the main peak of the M-giant stars and the red tail of the C stars. A comparison of the theoretical isochrone models with the observed color distribution indicates that most of the bright M-giant stars in NGC 205 were formed at log(t_yr_)~9.0-9.7. The logarithmic slope of the M_Ks_ luminosity function for M-giant stars was estimated to be 0.84+/-0.01, which is comparable with dwarf elliptical galaxies NGC 147 and NGC 185. Furthermore, we found that the logarithmic slopes of the M_Ks_ luminosity function for C and M-giant stars are different to places, implying a different star formation history within NGC 205. The bolometric luminosity function for M-giant stars extends to M_bol_=-6.0mag, and that for C stars spans -5.6