Most toughening methods for epoxy resins are usually used at the expense of other properties. Some polyhedral oligomeric silsesquioxanes (POSSs) with both a rigid Si-O-Si structure and flexible organic chain segments could be expected to be effective toughening agents. In this study, three reactive polyhedral oligomeric silsesquioxanes with a thiol group (OMPPS), a carboxyl group (OCOPS), and an epoxy group (OGCPS) were synthesized and characterized. They were utilized as modifiers to toughen 3-(oxiran-2-ylmethoxy)-N,N-bis(oxiran-2-ylmethyl)aniline (AFG-90MH)/4,4′-methylenebis(2-ethylaniline) (MOEA) (epoxy resin) with different molar ratios to obtain hybrid resins named OMPPS-EP-i, OCOPS-EP-j, and OGCPS-EP-k. The effects of the amount of modifier added and the length of the organic chain on the cage structure on various properties of the hybrid resins were investigated. The results show that all three modifiers show good compatibility with the epoxy resin. The hybrid resins have a low viscosity at 45~85 °C and can be cured at a low temperature (110 °C). The cured hybrid resins display improved toughness. Typically, the critical stress intensity factor (KIC) and impact strength of OGCPS-EP-0.6-C are 2.54 MPa∙m−1/2 and 19.33 kJ∙m−2, respectively, which increased by 58.75% and 22.48% compared with the pristine epoxy resin, respectively. In addition, the glass transition temperature and flexural strength of the hybrid resins are basically unchanged.