The structural, magnetic, electronic, dynamical and thermodynamic properties of PuN have been studied within the frameworks of the density-functional theory, DFT+U and hybrid DFT. The calculations have been performed using the full-potential-linearized augmented plane-wave method. The ferromagnetic and antiferromagnetic configurations are considered in this work. The lattice constants, bulk moduli, densities of states, and thermodynamic data have been computed and compared to available experimental data and other theoretical calculations published in the literature. Total energy results obtained with DFT+U and hybrid DFT indicate that the ground state of PuN is antiferromagnetic, in agreement with experiment. The chemical bonds between Pu and N have a mixture of covalent and ionic components, but the ionic character is stronger than covalent character. The phonon dispersion curves and the optical-mode frequencies are also reported. At last, the effect of spin-orbit coupling on the structural, magnetic, and electronic properties of PuN has been discussed.