  The chaos bound in the near-horizon regions has been studied through the
expansions of the metric functions on the horizon. In this paper, we
investigate the chaos bound in the the near-horizon region and at a certain
distance from the horizon of a charged Kiselev black hole. The value of the
Lyapunov exponent is accurately calculated by a Jacobian matrix. The angular
momentum of a charged particle around the black hole affects not only the
exponent, but also the position of the equilibrium orbit. This position
gradually moves away from the horizon with the increase of the angular
momentum. We find that the the bound is violated at a certain distance from the
horizon and there is no violation in the near-horizon region when the charge
mass ratio of the particle is fixed. The small value of the normalization
factor is more likely to cause the violation.
