The nature of surface vacancy in two-dimensional (2D) lead halide perovskites (LHPs) including 2D CsPbBr₃ has not been fully understood so far although the defects may play important roles in the optoelectronic properties of semiconductor materials. Some researchers claim that the defects in 2D LHPs, like in 3D LHPs, cannot form deep trap states, while some other researchers insist that there are mid-gap states induced by defects in 2D LHPs. In this work, the properties of surface Br vacancy in 2D CsPbBr₃ were studied by first principles methods, and specially, the optical transitions concerned with the surface Br vacancy were also studied. The results show that with the thickness of 2D CsPbBr₃ increasing, the defect level in energy bands and the charge transition energy level ∊(0/1+) become shallower. This trend is consistent with the results in bulk CsPbBr₃ reported before. However, the surface Br vacancy may have no clue in luminescence spectrum due to strong lattice relaxation. It may act as a nonradiative recombination center leading to negative effect on the optoelectronic performance of 2D CsPbBr₃ hence the surface passivation would be necessary indeed. This work could provide some constructive insights for further studies on 2D LHPs.