  We investigate the stability of $f(R)$-rotating (Kerr) black hole obtained
from a limited form of $f(R)$ gravity. In order to avoid the difficulty of
handling fourth order linearized equations, we transform this form of $f(R)$
gravity into the scalar-tensor theory by introducing two auxiliary scalars. In
this case, the linearized curvature scalar equation leads to a massive scalaron
equation. It turns out that the $f(R)$-rotating black hole is unstable because
of the superradiant instability known as the black-hole bomb idea.
