The effect of annealing on the 3.31 eV (A line) emission in ZnO nanorods is studied in detail by temperature-dependent photoluminescence (PL). Annealing results in obvious changes in peak energy and lineshape of the A line, indicating different luminescence origin in the as-grown and annealed ZnO nanorods. In the as-grown nanorods, the A line is a result of competition between free-to-neutral acceptor (FA) transition and the first longitude optical phonon replica of free exciton (FX-1LO) recombination. While for the annealed nanorods, FA transition disappears and the A line is attributed to FX-1LO only. In combination with trace impurity analysis, the results allow us to conclude that the acceptor involved in the FA transition is stacking faults rather than unintentional acceptor impurities.