In this study, electronic properties of armchair silicene nanoribbon perforated with periodic nanoholes are studied by first-principle calculations based on density functional theory. It has been demonstrated that pristine armchair silicene nanoribbons can be categorized into three branches with width W= 3P-1, 3P, and 3P+1, where P is a positive integer. Their energy gaps decrease as a function of increasing nanoribbon width and satisfy EG (3P-1) <; EG (3P) <; EG (3P+1). The bandgaps of armchair silicene nanoribbons perforated with periodic nanoholes show an oscillatory behavior and become smaller or larger than that of pristine armchair silicene nanoribbon depending on the nanoribbon's width and repeat periodicity of nanoholes. Results indicate that the different nanoribbons width and edge shape between two adjacent nanoholes and between nanoholes and nanoribbons in a small repeat periodicity will result in different quantum confinement effects. It has been also shown that the bandgap of armchair silicene nanoribbon are closely dependent on the position of nanoholes relative to edges of the nanoribbons.