The　spectroscopy　of　a　weakly　isolated　horizon　has　been　investigated.　We　obtain　an　equally　spaced　entropy　spectrum　with　its　quantum　equal　to　the　one　given　by　Bekenstein　(Phys　Rev　D　7:2333,　1973).　We　demonstrate　that　the　quantization　of　entropy　and　area　is　a　generic　property　of　horizons　which　exists　in　a　wide　class　of　spacetimes　admitting　weakly　isolated　horizons.　Our　method　based　on　the　tunneling　method　also　indicates　that　the　entropy　quantum　of　black　hole　horizons　is　closely　related　to　Hawking　temperature.