  Let $G$ be a connected center-free simple real algebraic group of rank one
and $\Gamma < G$ be a Zariski dense torsion-free convex cocompact subgroup. We
prove that the frame flow on $\Gamma \backslash G$, i.e., the right translation
action of a one-parameter subgroup $\{a_t: t \in \mathbb R\} < G$ of semisimple
elements, is exponentially mixing with respect to the Bowen-Margulis-Sullivan
measure. The key step is proving suitable generalizations of the local
non-integrability condition and non-concentration property which are essential
for Dolgopyat's method. This generalizes the work of Sarkar-Winter for $G =
\operatorname{SO}(n, 1)^\circ$ and also strengthens the mixing result of Winter
in the convex cocompact case.
