In this study, based on two attractive energetic compounds pentazole (PZ) and tetraazacubane (TAC), a new family of high energy and high nitrogen compounds pentazolyltetraazacubanes were designed. Then, a different number of NH2 or NO2 groups were introduced into the system to further adjust the property. The structures, properties, and the structure-property relationship of designed molecules were investigated theoretically. The results showed that all nine designed compounds have extremely high heat of formation (HOF, 1226-2734 kJ/mol), good density (1.73-1.88 g/cm3), high detonation velocity (8.30-9.35 km/s), high detonation pressure (29.8-39.7 GPa) and acceptable sensitivity (△V: 41-87 ?3). These properties could be effectively positive adjusted by replacing one or two PZ rings by NH2 or/and NO2 groups, especially for the energy and sensitivity performance, which were increased and decreased obviously, respectively. As a result, two designed pentazolyltetraazacubanes were predicted to have higher energy and lower sensitivity than the famous high energy compound in use 1,3,5,7-tetranitro-1,3,5,7-tetraazacyclooctane, while two others have better combination property than 1,3,5-Trinitro-1,3,5-triazacyclohexane. In all, four new pentazolyltetraazacubanes with good combination performance were successfully designed by combining PZ with TAC, and the further property adjustment strategy of introducing a suitable amount of NH2/NO2 groups into the system. This work may help develop new cage energetic compounds.