The stability of two-dimensional (2D) graphene-like GaAs is theoretically verified by the first-principles method based on the density functional theory (DFT) and the molecular dynamics (MD). The energy band structure, density of states (DOS), and parameters for describing optical properties of 2D GaAs are calculated. The results show that, two-dimensional GaAs is different from three-dimensional GaAs, and it shows a metallic property because the two highest bands are overlapping. The dimension reduction results in the enhancement of the interaction among electrons in s and d states of As. More DOS peaks occur with peak position shifts towards a low energy direction. The lower energy bands are composed of Ga-d, As-s and As-p states, and the higher energy bands are composed of As-s and As-p states. The 2D GaAs has a static permittivity of 3.67, and has a strong absorption for ultraviolet light. It shows a metallic reflection characteristic in the photon energy ranges of 3.90-4.71 eV and 5.69-6.90 eV.