We present a strong correlation of the gamma-ray (above 100 MeV) mean spectral indices aγ and X-ray (1 keV)mean spectral indices cX for 34 gamma-ray-loud blazars (16 BL Lac objects and 18 flat spectrum radio quasars). Astrong correlation is also found between the gamma-ray flux densities F-γ and X-ray flux densities Fx in the low state for 47 blazars (17 BL Lac and 30 flat spectrum radio quasars). Possible correlation on the gamma-ray emission mechanism is discussed. We suggest that the main gamma-ray radiation mechanism is probably the synchrotron process. The gamma-ray emission may be somewhat different from that of BL Lac objects and flat spectrum radio quasars.