A novel composite containing CoSe and porous carbon polyhedra (PCP), denoted as CoSe@PCP, was successfully synthesized using Co-based zeolitic imidazolate framework (ZIF-67) as precursor through a two-step method, including carbonization of ZIF-67 and subsequent selenization. The field-emission scanning electron microscopy and transmission electron microscopy characterizations confirm that CoSe nanoparticles are uniformly dispersed in PCP. When the CoSe@PCP was used as anode material for lithium-ion batteries, it exhibits superior performance with a high reversible capacity of 675 mAh g(-1) at 200 mA g(-1) after 100 cycles and 708.2 mAh g(-1) at 1 A g(-1) after 500 cycles as well as excellent cycling stability. Additionally, the CoSe@PCP also demonstrates excellent performance as anode material for sodium-ion batteries. A reversible capacity of 341 mAh g(-1) can be obtained over 100 cycles at 100 mA g(-1) with high cycling stability. The excellent battery performance of CoSe@PCP should be attributed to the synergistic effect of nanostructured CoSe and PCP derived from ZIF-67, in which the nanostructured CoSe possesses high reactivity towards lithium and sodium ions and the PCP can provide a continuous conductive matrix to facilitate the charge transfer and an effective buffering to mitigate the structure variation of CoSe during cycling. (C) 2017 Elsevier B.V. All rights reserved.