Antimonene, a new group-VA 2D semiconducting material beyond phosphorene, was recently synthesized through various approaches and was shown to exhibit a good structural integrity in ambient conditions and various interesting properties. In this work, we perform systematical first-principles investigations on the interactions of antimonene with the small molecules CO, NO, NO2, H2O, O2, NH3 and H2. It is found that NO, NO2, H2O, O2, and NH3 serve as charge acceptors, while CO shows a negligible charge transfer. H2 acts as a charge donor to antimonene with the amount of charge transfer being ten times that of H2 on phosphorene. The interaction of the O2 molecule with antimonene is much stronger than that with phosphorene. Surprisingly, the kinetic barrier for the splitting of the O2 molecule on antimonene is low (~0.40 eV), suggesting that pristine antimonene may undergo oxidation in ambient conditions, especially at elevated temperatures. Fortunately, the acceptor role of H2O on antimonene, opposite to a donor role in phosphorene, helps to suppress further structural degradation of the oxidized antimonene by preventing the proton transfer between water molecules and oxygen species to form acids. By comparing antimonene with phosphorene and InSe, we suspect that the acceptor role of water may be a necessary condition for a good environmental stability of such 2D layers to avoid structural decomposition. While the surface oxidation layer may serve as an effective passivation layer from further degradation of the underlying layers, our findings show that antimonene layers still need to be separated or properly protected by other noncovalent functionalization from oxygen or other environmental molecules. The present work reveals interesting insights into the environmental effects of physisorbed small molecules on the oxidation tendency and stability of antimonene, which may be important for its growth, storage and applications.