To explore promising energetic molecular species with huge energy release and significant kinetic stability, the singlet and triplet potential energy surface of nitrogen-rich compound PN₃ were constructed at the CCSD(T)/aug-cc-pVTZ//M06-2X/6-31+G(d,p) level.The computations performed identified 13 isomers and 21 transition states. The ground state isomer was the chain-like triplet PNNN(C_s). The kinetic stability of PN₃ was further evaluated by studying the dissociation, isomerization as well as the Born-Oppenheimer molecular dynamic (BOMD) simulations at the B3LYP/6-31+G(d) level. The results indicated that the chain-like triplet PNNN(C_s) and the tetrahedral-like singlet PN₃(C_3v) are both kinetically stable.