In the present study, a novel strategy for constructing new cage energetic compounds with both high energy and low sensitivity was proposed. That is to use a 3D nitrogen-rich cage compound as the core parent molecule to set the basis for obtaining high energy, followed by the introduction of a moderate number of nitro groups into the cage, which are linked with the carbon atoms to further improve the energy without increasing the sensitivity obviously and controlling the reaction difficulty caused by too many nitro groups as low as possible. The amino groups were introduced into the structure also to adjust the balance of energy and sensitivity. Finally, more importantly, the formation of nitrogen-rich cage and the introduction of nitro/amino groups were achieved synchronously by a typical and attractive one-step reaction (The Diels–Alder reaction) which possesses 100% atomic efficiency. Based on this strategy, six series of amino-substituted nitrogen-rich azoles were used as the dienes to react with different dienophiles like tetranitroethylene (TNE) to form the final cage products. From the theoretical investigation results, five optimal compounds (PA0, PB0, PC0, PE0, PE1) with low reaction energy barrier (11.2–31.6 kcal/mol) may set the high energy of CL-20 and low sensitivity of TNT together, and have been screened out as new advanced energetic compounds successfully. This study may provide a new feasible strategy and a unique perspective for developing new advanced energetic compounds.