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High-energy metal–organic frameworks (MOFs) based on nitrogen-rich ligands are an emerging class of explosives, and density is one of the positive factors that can influence the performance of energetic materials. Thus, it is important to design and synthesize high-density energetic MOFs. In the present work, hydrothermal reactions of Cu(II) with the rigid polynitro heterocyclic ligands 5,5′-dinitro-2H,2′H-3,3′-bi-1,2,4-triazole (DNBT) and 5,5′-dinitro-3,3′-bis-1,2,4-triazole-1-diol (DNBTO) gave two high-density MOFs: [Cu(DNBT)(ATRZ)3]n (1) and [Cu(DNBTO)(ATRZ)2(H2O)2]n (2), where ATRZ represents 4,4′-azo-1,2,4-triazole. The structures were characterized by infrared spectroscopy, elemental analysis, ultraviolet-visible (UV) absorption spectroscopy and single-crystal X-ray diffraction. Their thermal stabilities were also determined by thermogravimetric/differential scanning calorimetry analysis (TG/DSC). The results revealed that complex 1 has a two-dimensional porous framework that possesses the most stable chair conformations (like cyclohexane), whereas complex 2 has a one-dimensional polymeric structure. Compared with previously reported MOFs based on copper ions, the complexes have higher density (ρ = 1.93 g cm−3 for complex 1 and ρ = 1.96 g cm−3 for complex 2) and high thermal stability (decomposition temperatures of 323 °C for complex 1 and 333.3 °C for complex 2), especially because of the introduction of an N–O bond in complex 2. We anticipate that these two complexes would be potential high-energy density materials.