Display omitted •The P21/c-BaN3, P1¯-BaN4 and P1¯-BaN5 are energetically favorable under different pressures.•All three high-pressure structures contain six-membered rings consisting of NN single bond and NN double bond.•The P21/c-BaN3 was dynamically stable at ambient pressure, and it may be quenchable at ambient pressure after synthesis at high pressure.•The energy densities of P1¯4 and P1¯5 are comparable to that of TATB, RDX, and the detonation velocity and detonation pressure of the two structures are second only to TNT. Alkaline-earth metal nitrides have attracted widespread attention due to their promising potential for high energy–density materials. We predicted the new structures of N-rich BaNx (x = 3–5) compounds under high pressure and analyze their potential properties in this paper. The P21/c-BaN3 was discovered for the first time and it can exist stably when the pressure exceeds 100 GPa. Besides, both the new structures of P1¯-BaN4 and P1¯-BaN5 have lower energy values than the previously predicted structures at pressures of 90 GPa and 70 GPa, respectively. The three novel N-rich barium–nitrogen compounds are dynamically stable under high pressure conditions. Especially, it was found that the phase of P21/c-BaN3 can maintain dynamic stability at ambient condition by the AIMD. So, the P21/c-BaN3 is a metastable structure and it is not only synthesized at high pressure, but also can be quenched to ambient conditions. Moreover, the energy densities of P1¯-BaN4 and P1¯-BaN5 are equivalent to that of TATB, RDX, and the detonation velocity and detonation pressure of the two structures are second only to TNT. This paper provides important help for the research of N-rich alkaline earth metal Ba–N Compounds.