The high-pressure phase diagram of Co-N compounds is enriched by proposing five stable phases (Pnnm-Co2N, Pmn21-Co2N, Pmna-CoN, Pnnm-CoN2, and P1̅-CoN4) and two metastable phases (P3̅1c-CoN8 and P1̅-CoN10). A systematic study has been performed for revealing the novel polymeric nitrogen structure and the outstanding properties of predicted polynitrides, such as structural characterization, energy analysis, stability analysis, and electronic analysis. P3̅1c-CoN8 with the novel layer-shaped N-structure and P1̅-CoN10 with the novel band-shaped N-structure are first reported in this work. Moreover, P3̅1c-CoN8 (6.14 kJ/g) and P1̅-CoN10 (5.18 kJ/g) with high energy density can be quenched down to ambient conditions. The proposed seven high-pressure phases are all metallic phases. A weak ionic bond interaction is observed between the Co and N atoms, while a strong N-N covalent bond interaction is observed in the Pnnm-CoN2, P1̅-CoN4, P3̅1c-CoN8, and P1̅-CoN10 phases. The N atoms in the polynitrides hybridize in the sp2 state, for which the hybrid orbitals are constructed by the σ bond or lone electronic pair. The charge transfer between the Co and N atoms plays an important role to the structural stability. Moreover, the vibrational analysis of P3̅1c-CoN8 and P1̅-CoN10 phases is performed to guide the future experimental study.