We report optical studies of high-quality 1.3 μm strain-compensated GaInNAs/GaAs single-quantum-well structures grown by metalorganic vapor phase epitaxy. Photoluminescence excitation (PLE) spectroscopy shows clearly the electronic structure of the two-dimensional quantum well. The transition energies between quantized states of the electrons and holes are in agreement with theoretical calculations based on the band anti-crossing model in which the localized N states interact with the extended states in the conduction band. We also investigated the polarization properties of the luminescence by polarized edge-emission measurements. Luminescence bands with different polarization characters arising from the electron to heavy-hole and light-hole transitions, respectively, have been identified and verify the transition assignment observed in the PLE spectrum.