The molecular geometries and electronic structures of nitro derivatives of symmetric pyrazino-dicycloureas were obtained by a density functional theory (DFT) method with DFT-B3LYP/6-31G^**. Their values of theoretical molecular density (ρ) and heat of formation (HOF) were computed by quantum chemical method. The values of detonation velocity (D) and detonation pressure (p) were estimated using Kamlet-Jacobs equations. Studies on the relationship between structure and property of these nitro derivatives were performed. Results show that the number, positions, surrounding and symmetry of the nitro group within the molecule and the symmetry of the molecular structure are some principal factors affecting the thermal stabilities and detonation properties of nitro derivatives of symmetric pyrazino-dicycloureas. The values of ρ, HOF, D and p for 1,3,5,7-tetranitro-5, 7-dihydrodiimidazo[4,5-b:4'5'-e]pyrazine-2, 6(1H, 3H)-dione are 2.03 g·cm^-3, 265.63kJ·mol^-1, 9.08 km·s^-1, and 39.22 GPa, respectively. The structure of 1,3,5,7-tetranitro-2,6-dioxo-1,2,3,5,6,7-hexahydrodiimidazo[4,5-b:4'5'-e]pyrazine-4-oxide is unstable. These results obtained provide basic research data for molecular design and synthesis of novel high energetic density compounds (HEDC).