We analyzed metal organic vapor phase epitaxy growth mechanism of Ill-nitride semiconductors, GaN, A1N and InN based on first-principles calculations and thermodynamic analysis. With this calculated methods, we investigate the decomposition process of the group III source gases, X(CH3)3 (X = Ga, Al, In) at finite temperatures and whether the (CH3)3 AlNH2 adduct can be formed or not. Our calculated results show that (CH3)2 GaNH2 adduct cannot be formed in the gas phase reaction in GaN MOVPE. Whereas, (CH3)2AINH2 adduct can be formed so much in gas phase in A1N MOVPE. In case of GaN MOVPE, trimethylgallium (TMG, [Ga(CH3)3]) almost decomposes into Ga gas on growth surface by the assistance of H2 carrier gas instead of (CH3)2GaNH2 adduct formation. Moreover, in case of InN MOVPE, (CH3)2lnNH2 adduct formation cannot occur and it is relatively easy that In gas is produced even if there is no H2 carrier gas.