A facile method for the preparation of microwave absorbers with low density, high microwave absorptivity, and broad band is of paramount importance to the progress in practical application. Herein, commonly-used metal organic frameworks (MOFs) prepared just by mechanical stirring in methanol at room temperature were chosen as sacrificial templates to synthesize porous carbon composites with tunable dielectric and magnetic properties. With the replacement of Co atoms on the surface of zeolitic imidazolate framework-67 (ZIF-67) by Zn atoms, a Co-doped porous carbon composite with a low-dielectric amorphous carbon/Zn shell was constructed after annealing, leading to excellent impedance matching condition. Consequently, the as-obtained composite (Co/C@C-800) shows marvelous microwave absorption properties with an absorption capacity of −43.97 dB and a corresponding effective absorption bandwidth of 4.1 GHz, far exceeding that of the traditional porous carbon and composites directly derived from ZIF-67. The results provide a convenient way to modify MOFs for enhanced microwave absorption materials from the synergy of dielectric and magnetic losses.