Understanding the defect physics of ZnO is crucial in controlling its properties for various applications. We report the observation of an interesting 1.64 eV near-infrared (NIR) photoluminescence from ZnO and its evolution with annealing temperature. Based on a recent calculation on the transition levels of native point defects of ZnO [A. Janotti and C. G. Van de Walle, Phys. Rev. B 76, 165202 ( 2007)], the NIR emission can be successfully explained by the donor-acceptor transition between V-O and V-Zn and/or the radiative recombination of shallowly trapped electrons with deeply trapped holes at O-i.