A systematic high-pressure study of the CdNx (x = 2, 3, 4, 5, and 6) system is performed by using the first-principles calculation method in combination with the particle swarm optimization algorithm. We proposed four stable high-pressure phases (P4mbm-CdN2, Cmmm-CdN4, I4̅2d-CdN4, and C2/c-CdN5) and one metastable high-pressure phase (C2/m-CdN6), for which the structural frames are composed of a diatomic quasi-molecule N2, standard armchair N-chain, S-type bent armchair N-chain, zigzag-antizigzag N-chain, and N14 network structure. Among them, the novel zigzag-antizigzag N-chain and N14 network structure are reported for the first time. More importantly, Cmmm-CdN4 and C2/m-CdN6 possess high stability under ambient conditions, which may be quenched to ambient conditions once they are synthesized at high-pressure conditions. The high decomposition energy barrier (1.14 eV) results in a high decomposition temperature (2500 K) of Cmmm-CdN4, while a low decomposition energy barrier (0.19 eV) results in a mild decomposition temperature (500 K) of C2/m-CdN6. The high energy density and outstanding explosive performance make Cmmm-CdN4, I4̅2d-CdN4, C2/c-CdN5, and C2/m-CdN6 potential high-energy materials. The electronic structure analyses show that these predicted high-pressure structures are all metallic phases, and the N-N and Cd-N bonds are the strong covalent and ionic bond interactions, respectively. The charge transfer from the Cd atom plays an important role in the stability of the proposed structures.