To improve the quartz glass surface quality and optimize the process parameters, the influence of different polishing parameters on the material removal rate (MRR) and surface roughness in the process of quartz glass shear thickening polishing (STP) was studied. Experiments were designed based on the Taguchi method, and the MRR and surface roughness were used as evaluation conditions to analyze the effects of three key parameters, including polishing speed, abrasive concentration, and the slurry pH value on the STP process of quartz glass. The experimental results were evaluated by the signal-to- noise ratio, and the weight of each factor was calculated by the analysis of variance (ANOVA) method, and the optimal process parameter combination was obtained. As a result, the slurry pH value (41.85%) had the greatest impact on Sa, followed by the abrasive concentration (39.06%) and the polishing speed (19.09%). The abrasive concentration (63.78%) had the most significant effect on MRR, followed by polishing speed (28.81%) and the slurry pH value (7.41%). Under the optimal combination of polishing parameters, the polishing speed 100 r/min, the abrasive concentration 12%, the slurry pH value=8, the surface roughness Sa of the quartz glass decreased from (110±10) nm to (1.2±0.3) nm in 8 minutes’ polishing and the MRR reached 165.2 nm/min. Processing under optimized process parameters, STP can effectively remove scratches on the quartz glass surface and improve the surface quality of quartz glass. The STP method can be applied to the polishing of quartz glass plane and curved surface.