In this study, a magnetic/dielectric composite precursor is obtained by in situ growing zeolitic imidazolate framework-67 nanoparticles on the surface of acidified multi-walled carbon nanotubes (MWCNTs). After pyrolyzing the precursor in an argon atmosphere, a kind of nano-heterogeneous composite wave absorber was prepared. Subsequently, a new type of magnetic/dielectric wave-absorbing composite was prepared by heating and curing Co-C-MWCNTs and epoxy resin, and the properties of the composite were adjusted by changing the content of Co-C-MWCNTs. A variety of modern characterization methods were used to systematically study the micro-morphology, element composition and electromagnetic properties of the composite. The results show that after the combination of MWCNTs and Co-C particles with regular dodecahedron structure, a special synergistic effect appears. The addition of magnetic MOF derivatives not only improves the impedance matching characteristics of the composite and increases the magnetic loss mechanism, but also provides a new path for the transmission of electromagnetic waves because of its special pore structure and the three-dimensional network structure formed by cross-linking with MWCNTs. The interface polarization and multiple scattering effects greatly improve the attenuation efficiency of electromagnetic waves. In X-band (8-12 GHz), the Co-C-MWCNTs/EP composite with a loading of 17.5 wt% can achieve an effective absorption bandwidth of 2.38 GHz when the matching thickness is 1.6 mm. The combination of novel MOF-derived materials and traditional carbon materials is expected to provide new ideas for the design of composites with microwave absorption capabilities.