Three new nitrogen-rich energetic complexes Cu(DNABT)(NH₃)_2-x(NH₂NO₂)_x(x=0,1,2) were designed by incorporating N,N′-dinitroamino-bi(1,2,4-triazole) (DNABT) with copper, ammonia and nitramine. Their molecular, electronic and crystal structures, heat of formation, density, detonation performance and sensitivity were studied theoretically. The results show that the Cu and DNABT linked coordination bond is weaker than other bonds which possibly trigger the decomposition. The number of ammonia and nitramine ligands have a significant different effect on the structure and properties of the designed complex. All designed complexes possess high density (2.07-2.13 g·cm^-3), good energetic performance (detonation velocity: 8.44-9.12 km·s^-1, detonation pressure: 34.2-40.0 GPa) and acceptable sensitivity (7-22 cm), especially for the complex with x=1, whose energy is higher than RDXand similar sensitivity to RDX, being a potential high energy density compound.