The　quality　and　life　of　the　injected　product　are　affected　by　surface　quality　of　curved　mold,　and　reasonable　polishing　method　is　the　key　to　obtain　the　high-quality　surface　of　curved　mold.　Small　polishing　tool　is　controlled　by　constant　displacement　polishing　in　the　conventional　method　of　robot　polishing.　The　polishing　force　is　adjusted　to　affect　the　surface　quality　of　mold　during　mold　polishing.　The　shortcomings　of　traditional　control　method　of　robot　are　investigated　by　simulation,　and　the　constant　force　control　approach　is　proposed　to　maintain　stable　force,　which　is　achieved　by　a　position-based　impedance　control　algorithm.　The　polishing　experiments　of　curved　mold　are　conducted　by　using　two　control　methods　with　constant　displacement　control　polishing　(CDCP)　and　constant　force　control　polishing　(CFCP),　respectively.　The　experimental　results　show　that　the　CFCP　method　can　maintain　polishing　force　stability　and　the　reduction　of　surface　roughness　in　the　three　groups　of　experiments　using　CDCP　method　is　much　lower　than　that　of　CFCP　method,　respectively.　The　feasibility　of　constant　force　control　polishing　method　(CFCP)　is　verified.　©　2022,　The　Author(s),　under　exclusive　licence　to　Springer-Verlag　London　Ltd.,　part　of　Springer　Nature.