  We investigate the stability of black holes in the viable model of
$f(R)=R+R^2$ gravity which was known to be the best fit for inflation. These
include Schwarzschild and Kerr black holes. Instead of studying the
fourth-order linearized equation around the black hole background, we use the
corresponding tensor-scalar theory of the Starobinsky model to perform their
stability. The Schwarzschild black hole is stable, while the Kerr black hole is
unstable because of superradiant instability.
