This　paper　proposes　a　multi-person　action　recognition　system　based　on　frequency　modulated　continuous　wave　radar　(FMCW).　First,　a　Gaussian　mixture　model　clustering　method　(GMM)　is　used　to　extract　the　active　point　cloud　data　of　a　single　person　from　the　data　collected　by　the　radar.　Then　point　cloud　nearest　neighbor　sampling　algorithm　is　proposed　for　processing　the　radar　point　cloud　data.　Eventually,　the　long　and　short-term　memory　network　(LSTM)　is　used　to　extract　the　features　between　time　series　data　frames　to　realize　action　recognition.　In　this　paper,　a　nearest　neighbor　sampling　algorithm　is　proposed　to　solve　the　problem　of　sparse　point　cloud　in　single-person　activity　in　the　radar　point　cloud　data　processing.　This　method　selects　the　reflection　point　closest　to　the　centroid　of　the　current　frame　based　on　the　Euclidean　distance,　and　merges　multiple　frames　data　with　behavior　information　contained　through　a　sliding　window　to　fill　in　the　information　of　the　current　frame　and　enrich　the　temporal　and　spatial　sequence　data.　The　radar　point　cloud　data　collected　is　then　converted　to　fixed-dimensional　feature　information　to　meet　the　input　requirements　of　the　LSTM　network.　The　experimental　results　show　that　the　action　recognition　proposed　in　this　paper　has　an　average　recognition　accuracy　of　98.68%　for　falling,　sitting,　and　walking　in　a　multi-person　activity　scene.　©　2021　IEEE.