The decrease in electrical properties caused by the toughening of polypropylene (PP) is a difficult problem for the modification of PP used for cable insulation. In this research, an isotactic PP, a cross-linked polyethylene (XLPE) and two impact PP copolymers (IPCs) with an ethylene–propylene rubber phase content of 15 and 30% were prepared to assess the possibility of IPCs to be used as cable insulating material. The tensile properties and breakdown strength were evaluated, meanwhile, the rubber phase content dependence of the crystalline structure, morphology and trap distribution were also investigated. Results show that IPCs with a 15% rubber phase content (IPC15) can achieve the simultaneous improvement of elongation at break and breakdown strength compared with isotactic PP, which can be attributed to the special crystalline structure. According to the results of differential scanning calorimetry (DSC) and FTIR, it is proposed that the lamella thickness of IPC15 is maximal and some ethylene segments exist in PP crystals of IPC15 as crystalline structure defects, which is responsible for this enhanced breakdown strength. The morphology results reveal that rubber microspheres are found to coexist with spherulites, which can promote the relative sliding among lamellas under external force and further results in the increase in the elongation at break.