Abstract: In the process of ion-beam polishing solution of dwell time is very crucial. Such a solution is derived from the relation that the amount of material to be polished equals the processing function convolved with dwell time. The process of ion-beam polishing is just to deconvolve the relation. This inspires us to propose a new algorithm of stepwise elimination. The new algorithm requires less computer resources, runs faster, and yields adequate dwell-time function according to preset accuracy. We carried out simulations of polishing with two conventional methods and the new algorithm. The simulation results show that the values of PV diminish to 6.136nm, 33.347nm, and 3.875nm for the three methods, respectively, as compared to 363.721nm before polishing. It is notable that the accuracy of mirror surface has been greatly improved, particularly with the new method.