We find a significant anti-correlation between the hard X-ray photon index and the Eddington ratio L_Bol/L_Edd for a sample of Low-Ionization Nuclear Emission-line Regions (LINERs) and local Seyfert galaxies, compiled from literatures with Chandra or XMM-Newton observations. This result is in contrast with the positive correlation found in luminous active galactic nuclei (AGNs), while it is similar to that of X-ray binaries (XRBs) in low/hard state. Our result is qualitatively consistent with the spectra produced from advection dominated accretion flows (ADAFs). It implies that the X-ray emission of low-luminosity active galactic nuclei (LLAGNs) may originate from the Comptonization process in ADAF, and the accretion process in LLAGNs may be similar to that of XRBs in the low/hard state, which is different from that in luminous AGNs.