In this paper, we study the influence of the rewiring probability p of the directed small-world network on dynamical behavior of spiral wave using the Greenberg-Hastings cellular automaton model. The computer simulation results show that when p is small enough, the stable spiral wave under the regular networks keeps its stability unchanged, and when p is increased, the phenomenon such as meandering, breakup and disappearance of the spiral waves appears. The relation between the excitability and p leads to the conclusion that the occurrence of the above phenomenon originates from the reducing of the excitability. On the other hand, the period of cell is also related to p.