Crystals of Na+/Pr3+ beta-Al2O3 with different amounts of lanthanide ions have been investigated by optical spectroscopy methods between 4.2 K and 300 K. Optical absorption spectra in the visible region show three main features which are related to the H-3(4) --> P-3(0), H-3(4) --> P-3(1)(I-1(6)) and H-3(4) --> P-3(2) transitions. Polarized luminescence spectra have been recorded under cw excitation of various Ar+ ion laser lines. Complex emission spectra consisting of several, not fully resolved, components even at very low temperature, are observed for the P-3(0) --> H-3(4) transition between 20000 and 21000 cm-1. Excitation spectra and resonant fluorescence line narrowing (FLN) spectra of different components of this transition recorded at low temperature indicate the presence of, at least, two distinct sets of centers, in agreement with recent structural refinement results. Finally, we have evaluated the energy levels and crystal-field splittings by ligand-field calculations based on the angular overlap model (AOM). Our calculations reproduce the ground state splitting of Pr3+ ions in the beta-Al2O3 structure with different site symmetries.