In this study, density functional theory (DFT) is employed to investigate the electronic properties of armchair silicene nanoribbons perforated with periodic nanoholes (ASiNRPNHs). The dangling bonds of armchair silicene nanoribbons (ASiNR) are passivated by mono- (:H) or di-hydrogen (:2H) atoms. Our results show that the ASiNRs can be categorized into three groups based on their width: W = 3P − 1, 3P, and 3P + 1, P is an integer. The band gap value order changes from “EG (3P − 1) < EG (3P) < EG (3P + 1)” to “EG (3P + 1) < EG (3P − 1) < EG (3P)” when edge hydrogenation varies from mono- to di-hydrogenated. The energy band gap values for ASiNRPNHs depend on the nanoribbons width and the repeat periodicity of the nanoholes. The band gap value of ASiNRPNHs is larger than that of pristine ASiNRs when repeat periodicity is even, while it is smaller than that of pristine ASiNRs when repeat periodicity is odd. In general, the value of energy band gap for ASiNRPNHs:2H is larger than that of ASiNRPNHs:H. So a band gap as large as 0.92 eV is achievable with ASiNRPNHs of width 12 and repeat periodicity of 2. Furthermore, creating periodic nanoholes near the edge of the nanoribbons cause a larger band gap due to a strong quantum confinement effect.