Surface finish determines service life of glass workpieces. Therefore, an extensive polishing phase is usually performed to limit the local irregularities. In this paper, we propose to investigate the influence of the grinding parameters on the surface finish of glass samples in order to limit the damages at the earlier stage of the machining process. A central composite design of experiments has been used to define experimental tries that consist of up-grinding or down-grinding glass samples with various feed rate, depth of cut, and wheel speed values. Roughness parameters derived from the Abbott–Firestone curve Rk , Rvk , and the material ratio 100–Mr2 have been used to characterize the surface finishes of the ground glass samples. Using the design of experiments, surface responses have been modeled for each roughness parameter to investigate the influence of the cutting parameters. Abbott–Firestone parameters allow a relevant characterization of the glass samples surface finishes. Feed rate increase led to deeper valleys, thus providing a rough surface finish that could potentially shorten workpieces service life. On the contrary, increasing depth of cut tend to reduce valley depth. Wheel speed has shown minor influence on the surface finish. Up-grinding could help obtain less deep valleys than with a down-grinding. However, up-grinding also increases the cutting forces and induces vibrations that led to an increase of the core roughness and eventually to the fracture of the glass sample during the machining. In a material removal context—in opposition with polishing—feed rate should be carefully chosen since it is the most influential parameter on the surface finish. To maximize productivity while obtaining low-valleys surface finishes, an appropriate strategy would consist in down-grinding with a low feed rate, a high depth of cut, and a high wheel speed.