Nine isomers, twenty transition states, and some relative dissociation fragments of [C,N,N,P] system were located at the B3LYP/6-311G(d) and QCISD(t)/6-311+G(2df) (single-point) levels of theory, and the isomerization, structures, and stability of these obtained isomers were suggested. The results indicate that four nonlinear chainlike isomers NCNP, NCPN, CNPN, and CNNP with 2A′ electronic state are kinetically stable. Other isomers are kinetically unstable towards isomerization or dissociation because of the corresponding smaller reaction barriers. Furthermore, calculated vibrational frequencies, rotational constants, dipole moments, the first adiabatic ionization energies, and adiabatic electron affinities of the four isomers may provide some theoretical information that is helpful for identifying their existence in future laboratory and interstellar investigations. The results are also compared with [Si,N,N,P] system.