To date, breakdown voltage is an underlying risk to the epoxy-based electrical high voltage (HV) equipment. To improve the breakdown strength of epoxy resin and to explore the formation of charge traps, in this study, two types of polyhedral oligomeric silsesquioxane (POSS) fillers are doped into epoxy resin. The breakdown voltage test is performed to investigate the breakdown strength of neat epoxy and epoxy/POSS composites. Electron traps that play an important role in breakdown strength are characterized by thermally stimulated depolarized current (TSDC) measurement. A quantum chemical calculation tool identifies the source of traps. It is found that adding octa-glycidyl POSS (OG-POSS) to epoxy enhances the breakdown strength than that of neat epoxy and epoxycyclohexyl POSS (ECH-POSS) incorporated epoxy. Moreover, side groups of OG-POSS possess higher electron affinity (E_A) and large electronegativity that introduces deep-level traps into epoxy resin and restrain the electron transport. In this work, the origin of traps has been investigated by the simulation method. It is revealed that the functional properties of POSS side group can tailor an extensive network of deep traps in the interfacial region with epoxy and enhance the breakdown strength of the epoxy/POSS nanocomposite.