Laminated glass, as a typical kind of sandwich-structure composite, is widely used in various fields such as safety, vehicle and transportation engineering. Laminated glass mainly suffers from dynamic/impact loadings, and glass-ply cracking is the main failure pattern of laminated glass. This paper presents a non-local ordinary state-based peridynamic modeling and numerical approach for simulating the dynamic failure process of sandwiched laminated glass under low-velocity impact loading. The mechanical behavior of the PVB layer is simulated by reformulating classical visco-elastic model under the framework of ordinary state-based peridynamic theory, and the adhesion between the glass and PVB interlayer is described by using a penalty-based method. Fracture patterns of a laminated glass plate under drop-weight loading were investigated, and the numerical results compared well with experimental observations. Furthermore, a series of numerical simulations were conducted to in-depth analyze the effect of the thickness of the PVB interlayer and the glass layers on the fracture mode, initial locations and crack propagation speed of the laminated glass when subjected to impact.