Abstract In this paper, a novel fixed-abrasive lapping process to finish off-axis aspheric surfaces efficiently is proposed. The lapping mechanism of fused quartz glass was evaluated using the novel fixed-abrasive pad tool. The applied load and not the rotation speed and feed rate is the key factor affecting the material removal mode of fused quartz glass in the fixed-abrasive lapping process. Analysis of surface characteristic and subsurface damage indicates that lower applied load produces more ductile mode removal and that the removal on fused quartz glass can be changed from brittle fracture to ductile regime if the applied load is less than 25 N. The material removal rate (MMR) increases as the applied load is increased, which further increases the surface roughness. In addition, the MMR increases and the surface roughness decreases as the rotation speed is increased or the feed rate is deceased. A theoretical model for predicting the maximum SSD depth of the specimens during lapping was developed. The model can predict well that the maximum SSD depth increases with increasing applied load.