  We analyze the classical stability of Schwarzschild black hole in massive
conformal gravity which was recently proposed for another massive gravity
model. This model in the Jordan frame is conformally equivalent to the
Einstein-Weyl gravity in the Einstein frame. The coupled linearized Einstein
equation is decomposed into the traceless and trace equation when one chooses
$6m^2\varphi=\delta R$. Solving the traceless equation exhibits unstable modes
featuring the Gregory-Laflamme $s$-mode instability of five-dimensional black
string, while we find no unstable modes when solving the trace equation. It is
shown that the instability of the black hole in massive conformal gravity
arises from the massiveness where the geometry of extra dimension trades for
mass.
