Exploring whether cage-like molecular crystals similar to those in carbon systems exist in all-nitrogen systems is not only of great theoretical significance, but also of great practical application value as high-energy-density materials. Here, we predict a new type of cage-like all-nitrogen Td-N4 molecular crystal by using the CALYPSO method. The structure has mechanical and dynamic stability under ambient pressure. Moreover, Td-N4 molecular crystal has excellent thermal stability and can be stabilized to a high temperature of 2400 K. The reason why Td-N4 molecular crystal has such excellent stability is due to the high decomposition energy barrier (251.5 kJ/mol), and the most essential reason may be due to the strong double spherically aromatic of the molecule with the nucleus-independent chemical shift (NICS) of −70.5 ppm. It is worth noting that the energy density of the Td-N4 molecular crystal is 11.89 kJ/g, which is three times that of the TNT (4.3 kJ/g), twice that of HMX (5.7 kJ/g), and higher than that of the well-known cg-N structure (9.7 kJ/g). In addition, Td-N4 molecular crystal also has excellent properties with high Heat of detonation, detonation pressure and detonation velocity. The prediction of Td-N4 molecular crystal provides a very promising candidate for high energy density materials.