The instability of the spiral wave in an excitable medium is investigated by using the lattice Boltzmann method. The velocity distribution of the system are obtained by computer simulation, and discussed in connection with the pattern and the tip trajectory of the spiral wave. We find that the velocity of the particle at the rotating center of spiral wave changes periodically, while the change of this particles velocity is quickened and then becomes random when the spiral wave becomes unstable, which leads to the random decomposition of the velocity group and random distribution of velocity. The system falls into the spatiotemporal chaos finally.