Metal-organic-frameworks (MOFs) derived carbon or nitrogen-doped carbon (NC) materials are usually used as electromagnetic wave (EMW) absorbers. However, the effective control of the composition and structure of composites is still a major challenge for the development of high-performance EMW absorbing materials. In this work, core-shell structure and bimetallic composition Cu/nitrogen doped carbon @Co/ nitrogen doped carbon (Cu/NC@Co/NC) composites were designed and synthesized through the thermal decomposition of Cu-MOF@Co-MOF precursor. Cu/NC@Co/NC composites with different compositions were obtained by changing the ratio of Co-MOF and Cu-MOF. The composite (Cu/NC@Co/NC-3.75) prepared using 3.75 mmol of Co(NO)·6HO exhibits outstanding EMW absorption properties due to the optimized impedance matching and strong attenuation ability, which is caused by enhanced interfacial and dipolar polarization as well as multiple reflection and scattering. With the filler loading in paraffin of 35 wt%, the minimum reflection loss (RL) is up to -54.13 dB at 9.84 GHz with a thin thickness of 3 mm, and the effective absorption bandwidth (EAB, RL≤ - 10 dB) reaches 5.19 GHz (10.18-15.37 GHz) with the corresponding thickness of 2.5 mm. Compared with the Cu/NC and Co/NC, the Cu/NC@Co/NC-3.75 composite exhibits much better EMW absorbing performances caused by the bimetallic composition and the unique core-shell structure. This work provides a rational design for MOF-derived lightweight and broadband EMW absorbing materials.