  The chiral magnetic effect emerges from a miroscopic level, and its
interesting consequences have been discussed in the dynamics of the early
universe, neutron stars and quark-gluon plasma. An instability is caused by
anomalous electric current along magnetic field. We investigate effects of
plasma motion on the instability in terms of linearized perturbation theory. A
magnetic field can inhibit magnetohydrodynamic waves to a remarkable degree and
thereby affects the instability mode. We also found that the unstable mode is
consisted of coupling between Alfven and one of magneto-acoustic waves.
Therefore, the propagation of a mixed Alfven wave driven by magnetic tension is
very important. The direction of unperturbed magnetic field favors the wave
propagation of the instability mode, when Alfven speed exceeds sound speed.
