The work aims to solve the problem of difficulty in convergence of free surface polishing and improve the polishing efficiency of the polishing tool head. An offset fixed abrasive small polishing headis proposed. The theoretical model of removal function of the polishing tool head is established and simulation analysis is completed based on the structural characteristic parameters of the polishing tool head. Removal function experimental model of the polishing tool head is established and the rationality of the theoretical removal function of the polishing tool head is verified by point polishing experiments. Deterministic material removal model of workpiece surface is established based on the CCOS principle and effect of offset on polished surface of fixed abrasive tool headsurface shape convergence efficiency is evaluated by virtual machining experiment. The results show that the normalization theory removal function curve is in good agreement with the experimental curve removal function simulation model of point polishing can predict the removal contour shape of the fixed-point polishing spot. The surface shape error of the polishing tool head first increases and then decreases with the increase of the offset. The RMS convergence efficiency after polishing with the no-offset polishing tool head is 54.56%, and the PV convergence efficiency is 60.21%. The surface shape convergence efficiency after polishing reaches the maximum value when the offset of polishing tool head equals 1.5 mm. The RMS convergence efficiency of the surface shape error is 73.83%, and the convergence efficiency is 69.68%. The theoretical model of removal function of fixed abrasive tool head can guide deterministic material removal. The offset polishing tool head with an offset of 1.5 mm has the strongest ability to correct errors and can significantly improve the surface shape convergence efficiency of the fixed abrasive polishing process.