  We investigate effects of massive graviton on the rotation curves of the
Milky Way, spiral galaxies and Low Surface Brightness~(LSB) galaxies. Using a
simple de Rham, Gabadadze, and Tolley (dRGT) massive gravity model, we find
static spherically symmetric metric and a modified Tolman-Oppenheimer-Volkoff
(TOV) equation. The dRGT nonlinear graviton interactions generate density and
pressures which behave like a dark energy that can mimic the gravitational
effects of a dark matter halo. We found that rotation curves of most galaxies
can be fitted well by a single constant-gravity parameter $\gamma \sim
m_{g}^{2}C \sim 10^{-28}~{\rm m^{-1}}$ corresponding to the graviton mass in
the range $m_g \sim 10^{-21}-10^{-30} {\rm eV}$ depending on the choice of the
fiducial metric parameter $C\sim 1-10^{18}~\text{m}$. Fitting rotation curve of
the Milky Way puts strong constraint on the Yukawa-type coupling of the massive
graviton exchange as a result of the shell effects.
