We report an ab initio study on the rovibronic spectroscopy of the closed-shell diatomic molecule phosphorous mononitride, PN. The study considers the nine lowest electronic states, X 1Σ+, A 1Π, C 1Σ-, D 1Δ, E 1Σ-, a 3Σ+, b 3Π, d 3Δ and e 3Σ- using high level electronic structure theory and accurate nuclear motion calculations. The ab initio data cover 9 potential energy, 14 spin-orbit coupling, 7 electronic angular momentum coupling, 9 electric dipole moment and 8 transition dipole moment curves. The Duo nuclear motion program is used to solve the coupled nuclear motion Schrödinger equations for these nine electronic states and to simulate rovibronic absorption spectra of 31P14N for different temperatures, which are compared to available spectroscopic studies. Lifetimes for all states are calculated and compared to previous results from the literature. The calculated lifetime of the A1Π state shows good agreement with an experimental value from the literature, which is an important quality indicator for the ab initio A-X transition dipole moment.