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We study the dynamical evolution of a scalar field coupling to Einstein'stensor in the background of Reissner-Nordstr\"{o}m black hole. Our results showthat the the coupling constant $\eta$ imprints in the wave dynamics of a scalarperturbation. In the weak coupling, we find that with the increase of thecoupling constant $\eta$ the real parts of the fundamental quasinormalfrequencies decrease and the absolute values of imaginary parts increase forfixed charge $q$ and multipole number $l$. In the strong coupling, we find thatfor $l\neq0$ the instability occurs when $\eta$ is larger than a certainthreshold value $\eta_c$ which deceases with the multipole number $l$ andcharge $q$. However, for the lowest $l=0$, we find that there does not existsuch a threshold value and the scalar field always decays for arbitrarycoupling constant.

Dynamical evolution of a scalar field coupling to Einstein's tensor in the Reissner-Nordstr\"{o}m black hole spacetime