In　this　letter,　we　develop　a　matrix　reconstruction　algorithm-assisted　multi-carrier　differential　chaos　shift　keying　(DCSK)　scheme,　named　MRA-MC-DCSK　scheme.　Especially,　the　frequency-selective　fading　channel　is　considered　in　the　proposed　scheme.　We　establish　a　matrix　reconstruction　algorithm　(MRA)　to　reconstruct　the　information-bearing　signal,　which　can　solve　the　performance　deterioration　of　the　conventional　MC-DCSK　system　over　the　frequency　selective　fading　channels.　Moreover,　the　designed　MRA-MC-DCSK　system　can　achieve　the　frequency　diversity　by　the　reconstructed　transmitted　symbol.　We　further　analyze　the　theoretical　bit　error　rate　(BER)　expressions　of　the　designed　MRA-MC-DCSK　scheme　over　the　frequency　selective　multipath　Rayleigh　fading　channels.　Finally,　we　preform　various　Monte-Carlo　experiments　to　evaluate　the　performance　of　the　MRA-MC-DCSK.　Simulation　results　demonstrate　the　validity　of　the　BER　analysis　and　the　benefits　of　the　designed　MRA-MC-DCSK　scheme　over　the　conventional　MC-DCSK　scheme.