  We discuss stability issues of Schwarzschild black hole in non-local gravity.
It is shown that the stability analysis of black hole for the unitary and
renormalizable non-local gravity with $\gamma_2=-2\gamma_0$ cannot be performed
in the Lichnerowicz operator approach. On the other hand, for the unitary and
non-renormalizable case with $\gamma_2=0$, the black hole is stable against the
metric perturbations. For non-unitary and renormalizable local gravity with
$\gamma_2=-2\gamma_0={\rm const}$ (fourth-order gravity), the small black holes
are unstable against the metric perturbations. This implies that what makes the
problem difficult in stability analysis of black hole is the simultaneous
requirement of unitarity and renormalizability around the Minkowski spacetime.
