A series of organic–inorganic hybrid resin systems are prepared using hydroepoxy, 1,3-bis(aminomethyl)cyclohexane, and epoxy-functionalized polyhedral oligomeric silsesquioxane (POSS-Ep). The thermomechanical properties and shape-memory behaviors of the hybrid materials are systematically investigated by differential scanning calorimetry, thermogravimetric analysis (TGA), dynamic mechanical analysis, bend test, and shape recovery test. Results indicate that the glass transition temperature ( Tg) and rubber modulus gradually increase as the POSS-Ep content increases. The thermal stabilities of the hybrid materials gradually increase with increasing POSS-Ep content. The bend strength of the hybrid materials increases firstly and then decreases as POSS-Ep content increases, showing an extreme value for the hybrid materials with 3.17 mol% POSS-Ep content. Finally, investigation of the shape-memory behavior of the hybrid materials reveals that full recovery can be observed after only several minutes when the temperature is equal to or above Tg. The shape recovery time decreases at first and then increases as POSS-Ep content increases at Tg, Tg + 10°C, and Tg + 20°C. These results are attributed to the increase in POSS-Ep content.