The work aims to fully take advantages of fixed abrasive (FA) lapping /polishing. Fixed abrasive pads were employed to lap quartz glass, and material removal rate (MRR) and surface roughness (Ra) were chosen as the evaluation indicators. The influence of processing parameters on the machining performance of fixed abrasive lapping was investigated by using 3-factor and 3-level response surface method. The MRR model and the Ra model were developed. Combining the response surface method and its contour plot, the combined law of processing parameter and the optimal processing parameters under each target were obtained. Finally, the optimal processing parameters were verified. The results show that the best processing parameters for MRR are:rotation speed 90 r/min, load 20.685 kPa, slurry 60 mL/min, while those for surface roughness are:rotation speed 100 r/min, load 20.685 kPa, and slurry 80 mL/min. The predicted values of the models are 34.5 nm/min and 38.5 nm, in well accordance with those of verification experiment which are:37.6 nm/min and 39.4 nm. The comparison shows that the obtained model of processing parameter by response surface method has a very good predictive ability, the surface of machined work-piece at the optimized parameters is very smooth, and no obvious pits or coarse scratches are found.