In the process of computer controlled optical surfacing (CCOS), the uncontrollable rolled edge restricts further improvements of the machining accuracy and efficiency. Two reasons are responsible for the rolled edge problem during small tool polishing. One is that the edge areas cannot be processed because of the orbit movement. The other is that changing the tool influence function (TIF) is difficult to compensate for in algorithms, since pressure step appears in the local pressure distribution at the surface edge. In this paper, an acentric tool influence function (A-TIF) is designed to remove the rolled edge after CCOS polishing. The model of A-TIF is analyzed theoretically, and a control point translation dwell time algorithm is used to verify that the full aperture of the workpiece can be covered by the peak removal point of the tool influence functions. Thus, surface residual error in the full aperture can be effectively corrected. Finally, the experiments are carried out. Two fused silica glass samples of 100 mm×100 mm are polished by traditional CCOS and the A-TIF method, respectively. The rolled edge was clearly produced in the sample polished by the traditional CCOS, while residual errors do not show this problem the sample polished by the A-TIF method. Therefore, the rolled edge caused by the traditional CCOS process is successfully suppressed during the A-TIF process. The ability to suppress the rolled edge of the designed A-TIF has been confirmed.