The structure and spectroscopic properties of the ground and the lowest excited electronic states of the alkali hydride cation NaH+ have been investigated using an ab initio approach. In this approach, a nonempirical pseudopotential for the Na+ core has been used and a core–core and a core-valence correlation corrections have been added. The adiabatic potential energy curves and the molecular spectroscopic constants for numerous electronic states of 2Σ+, 2Π, and 2Δ symmetries, dissociating up to Na (4d) + H+ and Na+ + H (3d), have been calculated. As no experimental data are available, we discuss our results by comparing with the available theoretical calculations. A satisfying agreement has been found for the ground state with previous works. However, a clear disagreement between this study and the model potential work of Magnier (Magnier, J. Phys. Chem. A 2005, 109, 5411) has been observed for several excited states. Numerous avoided crossings between electronic states of 2Σ+ and 2Π symmetries have been found and analysed. They are related to the interaction between the potential energy curves and to the charge transfer process between the two ionic systems Na+H and NaH+. Furthermore, we provide an extensive set of data concerning the transition dipole moments from X2Σ+ and the 22Σ+ states to higher excited states of 2Σ+ and 2Π symmetries. Finally, the adiabatic potential energy curves of the ground (X2Σ+) and the first (22Σ+) excited states and the transition dipole moments between these states are used to evaluate the radiative lifetimes for the vibrational levels of the 22∑+ state for the first time. In addition to the bound–bound contribution, the bound-free term has been evaluated and added to the total radiative lifetime. © 2012 Wiley Periodicals, Inc.