In this work, an efficient cage-core peroxymonosulfate (PMS) catalyst was synthesized by applying an electrospinning–calcination process to the cobalt–zeolitic imidazole framework (ZIF-67) crystals for the catalytic degradation of dimethyl phthalate (DMP). The morphology and surface properties of the synthesized materials (ZIF-67, Z600 and ZP400/600/800) were well characterized. ZP600 showed great performance for the catalytic degradation of DMP in the initial pH range of 7.5–10.5. The removal rate of DMP could reach 90.4% in 60 min under optimum dosages of reagents (catalyst = 0.1 g/L, PMS = 0.5 mM, DMP = 6 ppm), and the mineralization degree of contaminant could reach 65%. By quenching experiments, it was determined that sulfate radical (SO4−·) and hydroxyl radical (·OH) dominated the degradation process. Moreover, due to the good magnetism, ZP600 could be easily separated from liquid and showed great reusability in five-cycle reaction experiments. Surprisingly, with the cover of cage-like polyacrylonitrile (PAN) fibers, the cobalt leaching amount of ZP600 decreased by about 87%. This study would expand the application of the electrospinning process in the development of functional materials for water purification.