This　paper　proposes　a　multi-carrier　differential　chaos　shift　keying　modulation　using　permutation　index　(PI-MC-DCSK)　over　multipath　fading　and　additive　white　Gaussian　noise　(AWGN)　channels,　by　exploiting　the　advantages　of　permutation　index　and　multi-carrier　modulations.　In　the　proposed　PI-MC-DCSK,　the　predefined　subcarriers,　can　carry　multiple　bits　associated　with　the　order　of　permutation　index,　which　can　achieve　high　energy　efficiency　as　compared　to　the　one　bit　carried　by　each　subcarrier　in　the　conventional　MC-DCSK.　At　the　transmitter,　the　first　predefined　subcarrier　stores　reference　data,　while　the　rest　carry　data　signal.　Then,　the　transmission　energy　of　the　system　can　be　significantly　saved.　At　the　receiver,　received　data　passes　through　the　multi-carrier　demodulator,　and　the　mapped　bits　are　estimated　by　the　correlators.　Simulation　results　show　that　the　proposed　PI-MC-DCSK　has　excellent　error　performance　and　provides　a　much　higher　data　rate　than　the　conventional　MC-DCSK.　©　2022　IEEE.