Laser pulses that enhance the predissociation reaction of NaI are theoretically studied based on a local control method. Two control schemes corresponding to two time regimes, one of subpicoseconds and one of a few picoseconds, are considered. For subpicosecond control, the pulse is designed to induce the Tannor-Rice pump-dump scheme, in which an intrapulse pump-dump process is predicted. The created wave packet has a high velocity to accelerate the nonadiabatic transition because of the Landau-Zener mechanism. On a longer time scale (several picoseconds), we employ a two-step control scheme. First, we use a variational procedure to determine the target wave packet that has the shortest lifetime at a given time. Then we calculate the control pulse to shape this target by a backward time propagation technique. Numerical results show that the wave packets generated by the control pulses are effective for accelerating the predissociation of NaI.