Metal-organic framework (MOF) nanocrystalline materials have received great attention because of their application in heterogeneous catalysis. However, they suffer from poor separation from reaction mixtures in practical applications. In this study, we report the first cobalt metal-organic framework containing zeolitic imidazolate framework (ZIF)-67 nanoparticles immobilized on electrospun polyacrylonitrile (PAN) nanofibers, which was used as a composite catalyst (ZIF-67/PAN) for activating peroxymonosulfate (PMS). Detailed characterization showed that the ZIF-67/PAN nanofibers possessed a flexible one-dimensional structure. To demonstrate the catalytic performance of the ZIF-67/PAN nanofibers, the activation of PMS for the catalytic degradation of acid yellow-17 (AY) was chosen as the model catalytic reaction. The results show that 95.1% of AY (500 mg L-1) was removed by ZIF-67/PAN in 10 min, which is much higher than many other PMS catalyst. More interestingly, the flexible ZIF-67/PAN composite nanofibers catalysts were not only easy to separate from solution but they also retained high catalytic stability. The influencing factors for PMS activation were also investigated, including the catalyst dosage, reaction temperature, solution pH, and doping with competing organic molecules. The degradation mechanism was elucidated by electron paramagnetic resonance experiments. This work provides a new sight into the fabrication of high-performance MOF catalysts with outstanding recycling properties, which may promote the use of MOF materials in more practical applications.