[en] We report that a band-tail emission at 3.08 eV, lower than near-band-edge energy, is observed in photoluminescence measurements of bulk Na-doped CuAlO_2. The band-tail emission is attributed to Na-related defects. Electronic structure calculations based on the first-principles method demonstrate that the donor-acceptor compensated complex of Na_A_l-2Na_i in Na-doped CuAlO_2 plays a key role in leading to the band-tail emission and bandgap narrowing. Furthermore, Hall effect measurements indicates that the hole concentration in CuAlO_2 is independent on Na doping, which is well understood by the donor-acceptor compensation effect of Na_A_l-2Na_i complex. (paper)