The two-dimensional (2D) semiconductor material of InSe has received much attention due to its excellent electrical properties and moderate adjustable bandgap. The vacancy defects in the material affect not only the optical and electrical properties, but also the environmental stability. Compared with other phases in InSe materials, δ-InSe has superior material properties, however, the effect of environment on this material stabilityhas not been reported. In this work, we systematically investigate the stability of 2D δ-InSe material under oxygen environment based on density functional theory. The results are shown below. Firstly, in an oxygen environment, the perfect δ-InSe surface exhibits good inertness and stability, for O₂ molecules need to overcome an exceptionally high energy barrier of 1.827 eV from physical adsorption to chemical adsorption on its surface. Secondly, the presence of Se vacancies (V_Se) promotes the oxidation reaction of δ-InSe, which only requires overcoming a low energy barrier of 0.044 eV. This suggests that the stability of δ-InSe in an oxygen environment is significantly reduced because of the presence of V_Se. The O₂ molecules oxidized δ-InSe monolayer is beneficial to the dissociation and adsorption of H₂O molecules. Finally, the oxidation rate of δ-InSe with In vacancies (V_In) is slower, with the adsorption energy and charge transfer involved in the physical adsorption of O₂ molecules on the V_In surface being similar to those on a perfect surface. The oxidation process needs to overcome a higher energy barrier of 1.234 eV. The findings of this study will provide theoretical guidance for better understanding the oxidation behavior of single vacancy defects in monolayer δ-InSe, and reference for experimental preparation of high-reliability 2D δ-InSe devices.