(CH3)3Al (TMA) has been employed for preparation of various thin films. It is also known to be hypergolic in the air. To unveil the hypergolic phenomenon, the mechanism for the reaction of TMA with O2 and/or H2O molecules is studied using computational quantum methods. Our results show that TMA reacts with water much faster than with O2, and water is not an efficient catalyst to help O2 reacting with TMA. The reactions of TMA with water and oxygen molecules can undergo subsequent ones in the air. However, the barrier predicted for production of CH3 was found to be too high for combustion initiation under the ambient condition.