J, H and K' images obtained with the Canada-France-Hawaii Telescope were used to investigate the stellar contents of the asymptotic giant branch (AGB) in the dwarf elliptical galaxy NGC 185. The bright parts of (K, J-K) and (K, H-K) color-magnitude diagrams consist of a group of bright blue stars, a dominant population of M-giants and a red C star population. There were 73 C stars with a mean magnitude of <K> = 16.26±0.38, corresponding to <MK> = -7.93, and mean colors of <(J-K)0> = 2.253 and < (H-K)0> = 0.865. The number ratio of C stars to M-giants was estimated to be 0.11±0.04 without any radial gradient from the center of NGC 185. The (J-K) and (H-K) color distributions of AGB stars showed an M-giant peak and blue and red tails, where the latter two correspond to AGB stars younger than those along M-giant peak and C stars. The bolometric luminosity functions of M-giants and C stars indicate that the M-giant AGB sequence has terminated at Mbol = -6.2, while the most luminous C star has Mbol = -5.5. The bolometric luminosity function of C stars in NGC 185 is very similar to that of recent literature values derived from Vi band photometry. The logarithmic slope of the luminosity function for bright M-giant stars was estimated to be 0.83±0.02 in K band. Theoretical isochrone models, compared with the observed near-infrared photometric properties of AGB stars, indicate that star formation in NGC 185 has a wide range of ages with possibly two different epochs of star formation.