In　this　paper　an　efficient　grinding　mode　which　is　employed　by　the　Cranfield　BoX　ultra　precision　grinding　machine　is　discussed.　The　equations　of　workpiece　surface　and　grinding　wheel　surface　are　proposed　and　the　grinding　motion　is　simulated　via　Matlab.　The　trajectory　of　the　changing　cutting　region　is　discussed.　The　simulation　results　show　that　this　grinding　mode　is　suit　to　manufacture　low　slope　surfaces.　Generally,　the　workpiece　surface　is　steeper,　and　the　cutting　range　of　the　machine　is　smaller.　The　angle　of　the　spindle　inclination,　the　grinding　wheel　width　and　the　cutting　depth　should　be　chose　properly　for　different　manufacturing　capacity.