The　traditional　S　type　acceleration/　deceleration　algorithm　in　CNC　system　is　not　suitable　for　high-speed　motion　due　to　the　mutation　of　jerk.　A　flexible　acceleration/deceleration　algorithm　suitable　for　high-speed　motion　system　was　introduced,　in　which　the　velocity,　acceleration,　jerk　and　displacement　were　all　consecutive　and　the　values　of　jerk　at　the　beginning　and　end　point　were　zero.　Compared　with　traditional　trigonometric　function　algorithms,　the　proposed　algorithm　was　more　flexible　and　could　give　full　play　to　the　maximum　acceleration　performance　of　CNC　machine　tool.　Displacement　adaptation　method　and　interval　discrimination　method　were　proposed　to　plan　the　acceleration　and　deceleration　mode.　The　interval　discrimination　method　could　quickly　find　the　interval　of　velocity　value　by　a　few　simple　calculations.　The　acceleration　and　deceleration　curve　parameters　could　be　obtained　by　solving　quadratic　equation　only　once,　which　ensured　the　high　efficiency.　This　algorithm　was　analyzed　and　discussed　with　MATLAB.　Through　experiment,　the　smooth　continuous　acceleration　and　velocity　curve　were　obtained,　which　proved　the　accuracy　and　the　feasibility　of　the　proposed　algorithm.　©　2019,　Editorial　Department　of　CIMS.　All　right　reserved.