Edge effect seriously restricts the processing accuracy and efficiency of CCOS， which is one of the technical difficulties needed to be solved urgently. An important approach to solve this problem is to establish a quantitative removal model of tool pad based on the Preston equation on the edge of the workpiece. The model includes some process parameters such as the workpiece size， the tool pad size， the processing pressure， velocity， time and position. The model calculates accurately the edge pressure distribution and the processing cumulative time. The processing pressure increases exponentially with the edge exposure area of the tool pad on the edge of the workpiece. The accumulated processing time of workpiece presents stage variation with the central point of tool pad in different workpiece sections. A single shaft machine with numerical control function has been developed. Combining with the established model， the machine is used to control edge effect effectively. The scale coefficient k of Preston equation is worked out in the experiment firstly. The model is in good agreement with the actual experiment results， and the accuracy can reach to 91.9%. The edge effect control method with the CNC single shaft machine and the relative model are well in guiding the actual grinding and polishing process.