  We study the quantum chaos in the Bose-Fermi Kondo model in which the
impurity spin interacts with conduction electrons and a bosonic bath at the
intermediate temperature in the large $N$ limit. The out-of-time-ordered
correlator is calculated based on the Bethe-Salpeter equation and the Lyapunov
exponent $\lambda_L$ is extracted. Our calculation shows that the Lyapunov
exponent monotonically increases as the Kondo coupling $J_K$ increases, and it
can reach an order of $\lambda_L\sim T$ as $J_K$ approaches the $MCK$ point.
Furthermore, we also demonstrate that $\lambda_L$ decreases monotonously as the
impurity and bosonic bath coupling $g$ increases, which is contrary to the
general expectation that the most chaotic property occurs at the quantum
critical point with the non-Fermi liquid nature.
