  We investigate the massive graviton stability of the BTZ black hole obtained
from three dimensional massive gravities which are classified into the
parity-even and parity-odd gravity theories. In the parity-even gravity theory,
we perform the $s$-mode stability analysis by using the BTZ black string
perturbations, which gives two Schr\"odinger equations with frequency-dependent
potentials. The $s$-mode stability is consistent with the generalized
Breitenlohner-Freedman bound for spin-2 field. It seems that for the parity-odd
massive gravity theory, the BTZ black hole is stable when the imaginary part of
quasinormal frequencies of massive graviton is positive. However, this
condition is not consistent with the $s$-mode stability based on the
second-order equation obtained after squaring the first-order equation. Finally
we explore the black hole stability connection between the parity-odd and
parity-even massive gravity theories.
