  We study the circular motion of charged particles near a charged black hole.
The general form of the Lyapunov exponent of charged particles is obtained by
using the Jacobian matrix. The results show that the chaos bound can be
saturated by the circular motion of charged particles on the horizon. By
further expanding the Lyapunov exponent near the horizon and investigating
Reissner-Nordstr\"om(RN) black holes with different $M/Q$, we find that in
contrast to the static equilibrium, the circular motion of charged particles
can have a larger Lyapunov exponent due to the existence of angular momentum.
For the RN black holes which have the mass-charge ratio $1<M/Q <1.1547$, the
chaos bound is locally violated by the null and the time-like circular motion
with large angular momentum. As an illustration of the universality of our
results, we study the charged particles' circular motion near the
Reissner-Nordstr\"om Anti-de Sitter (RN-AdS) black hole and find that the null
and the time-like circular motion with large angular momentum can exceed the
chaos bound under the background of RN-AdS black holes with the mass-charge
ratio in the range $1.23132<M/Q<1.75225$.
