Multiple　tuned　mass　dampers　(TMDs)　are　superior　to　the　single　TMD　with　the　same　mass　in　the　bandwidth　and　effectiveness　for　vibration　control,　and　the　most　adopted　optimization　methods　for　TMDs　are　H∞　or　H2　(i.e.　minimization　of　the　amplitude　or　root　mean　squared　value　of　the　vibration).　However,　the　chatter　vibration　in　the　machine　tool　is　a　special　self-excited　problem.　Especially　for　turning,　the　chatter-free　depth　of　cut　is　only　determined　by　the　negative　real　part　of　the　relative　frequency　response　function　(FRF)　between　the　tool　and　workpiece.　The　objective　function　of　multiple　TMDs　damping　the　primary　structure　was　formulated　(i.e.　maximizing　the　most　negative　point　of　tool　point　FRF),　and　the　minimax　approach　was　employed　to　optimize　the　stiffness　and　damping　of　each　TMD.　The　advantage　of　the　proposed　method　was　validated　by　tuning　three　TMDs　on　a　specially　designed　fixture　of　a　turning　machine　after　performing　the　modal　test.　The　cutting　tests　demonstrate　that　the　tuning　method　can　further　increase　the　chatter　suppression　performance　of　multiple　TMDs,　and　the　chatter　free　depth　of　cut　can　be　increased　52%　more　than　the　H∞　method.