Due to the brittleness, monolithic glass may fracture under impact, resulting in catastrophic sequences. The combined finite-discrete element method, i.e., FDEM, is employed to investigate both the oblique and the perpendicular impact failures of monolithic glass parametrically, particularly the soda-lime glass. Using FDEM, glass is discretised into discrete elements where a finite element formulation is incorporated, leading to accurate evaluation of the contact forces and structural deformation. Following the basic theories of the FDEM, a cohesive Mode I fracture model of glass is briefly introduced. Numerical examples are given for the verification of the employed fracture model and the applicability of the FDEM, and comparisons have been made against the computational and experimental results in the literature. The investigated parameters include the impact velocity, the impact angle, the material properties of glass, etc. The obtained results not only revealed the impact fracture mechanism of soda-lime glass but also provided guidance for its design and manufacturing.