The　spectroscopy　of　the　apparent　horizon　of　Vaidya　black　holes　is　investigated　via　adiabatic　invariance.　We　obtain　an　equally　spaced　entropy　spectrum　with　its　quantum　equal　to　the　one　given　by　Bekenstein　[J.　D.　Bekenstein,　Phys.　Rev.　D　7,　2333　(1973)].　We　demonstrate　that　the　quantization　of　entropy　and　area　is　a　generic　property　of　horizon,　not　only　for　stationary　black　holes,　and　the　results　also　exit　in　a　dynamical　black　hole.　Our　work　also　shows　that　the　quantization　of　black　hole　is　closely　related　to　the　tunneling　formalism　for　deriving　the　Hawking　effect,　which　is　interesting.