Periodic dispersion corrected density functional theory (DFT) calculations were carried out to examine the Hirshfeld surface, two dimensional (2D) fingerprint plots, crystal structure, molecular structure and density of state of all-nitrogen pentazolate anion complex [Co(H2O)4(N5)2]·4H2O under hydrostatic pressure from 0 to 20 GPa. The GGA/PW91-OBS method was applied in the present study. The intercontacts in [Co(H2O)4(N5)2]·4H2O were analyzed by Hirshfeld surfaces and 2D fingerprint plots. With ascending pressure, the lattice constants, compression rates, bond lengths, bond angles, and density of states change irregularly. Under 11.5, 13.0 and 15.8 GPa, covalent interaction competition is obvious between Co-N and Co-O bonds. It is possible to achieve orderly modification and regulation of the internal structure of [Co(H2O)4(N5)2]·4H2O by applied pressure. This is in accordance with the results from density of states analysis. The external compression causes the nonuniformity of electron density and the differential covalent interaction between pentazolate anion, coordinated water and atom Co. It is of great significance to interpret inter/intramolecular interaction and structural stability of [Co(H2O)4(N5)2]·4H2O and provide theoretical guidance for the design of metal complexes of all-nitrogen pentazolate anion.