  We investigate the new massive conformal gravity which is not invariant under
conformal transformations, in comparison to the massive conformal gravity. We
find five polarization modes of gravitational waves propagating on the
Minkowski spacetimes. The stability of Minkowski spacetimes is guaranteed if
the mass squared is not negative and the linearized Ricci tenor is employed to
describe a massive spin-2 graviton. However, the small Schwarzschild black hole
is unstable against the $s$-mode massive graviton perturbations.
