  We study the dynamical evolution of a scalar field coupling to Einstein's
tensor in the background of Reissner-Nordstr\"{o}m black hole. Our results show
that the the coupling constant $\eta$ imprints in the wave dynamics of a scalar
perturbation. In the weak coupling, we find that with the increase of the
coupling constant $\eta$ the real parts of the fundamental quasinormal
frequencies decrease and the absolute values of imaginary parts increase for
fixed charge $q$ and multipole number $l$. In the strong coupling, we find that
for $l\neq0$ the instability occurs when $\eta$ is larger than a certain
threshold value $\eta_c$ which deceases with the multipole number $l$ and
charge $q$. However, for the lowest $l=0$, we find that there does not exist
such a threshold value and the scalar field always decays for arbitrary
coupling constant.
