Zeolite imidazolate frameworks (ZIFs) derivatives, porous N-doped carbon (CN) materials, show outstanding performance when used as catalyst supports. The characteristics of ZIFs affect significantly the microstructure of CN. In this work, a series of CN materials were fabricated through direct pyrolysis of Zn/Co-ZIFs and Pd@CN catalysts were achieved by loading Pd nanoparticles. The results underline that the Co content in Zn/Co-ZIFs influences considerably the properties of CN and the catalytic activity of Pd@CN for the phenol hydrogenation to cyclohexanone. N-2 adsorption-desorption, CO2-TPD, and ICP analyses confirm that the increase of Co in ZIFs can enhance significantly the mesoporous ratio of CN for improving the loading and dispersion of Pd and increase the basic sites of CN materials for improving the phenol adsorption. As a result, significantly enhanced phenol conversion with similar cyclohexanone selectivity is achieved. These findings provide deep insights for the fabrication of ZIF-derived CN materials and their applications in catalysis.