The structural stability of CeN under hydrostatic compression has been analyzed theoretically. The comparison of enthalpies calculated as a function of hydrostatic compression for rocksalt type (B1), tetragonal (B10), and CsCl type (B2) structures suggests that the B1 phase will transform to B10 structure at $53 GPa, which upon further compression will transform to B2 phase at $200 GPa. However, the static high pressure energy dispersive x-ray diffraction measurements on CeN by Olsen et al. [J. Alloys Compd. 533, 29 (2012)] report that the B1 phase transforms directly to B2 phase at $65 GPa. To resolve the discrepancy between our calculations and experimental results, we have performed lattice dynamic calculations on these structures. The phonon spectra calculated at zero pressure correctly show B1 phase to be dynamically stable, and B10 and B2 to be unstable. At 60 GPa, the B1 phase becomes dynamically unstable and the B10 structure emerges as a dynamically stable phase whereas B2 still remains unstable. At still higher pressure of !200 GPa, the B2 phase becomes not only the lowest enthalpy structure but also dynamically stable. These findings support the results of our static lattice calculations. Further, our calculated angle dispersive x-ray diffraction pattern of B1, B10, and B2 phases shows that most of the diffraction peaks of B10 phase except few weak peaks coincide with the peaks of either B1 or B2 phase; which may pose a difficulty in unambiguously identifying the high pressure phase until a sufficient amount of B1 phase is transformed to the new structure so that the weak peaks, if present, are also visible.