  We propose an extension of the standard model (SM) with $U(1)_{\mu-\tau}$
gauge symmetry, extra vectorlike quark doublets $Q'_a$ and singlet scalar
$\chi$, both of which are charged under $U(1)_{\mu-\tau}$ and carry {odd} dark
$Z_2$ parity. Then assuming that $\chi$ is the dark matter (DM) of the universe
and imposing various constraints from dark matter search, flavor physics and
collider search for $Q'_a$, one can show that radiative corrections to
$b\rightarrow s Z^{'*} \rightarrow s l^+ l^- $ involving $Q'_a$ and $\chi$ can
induce $\Delta C_9 \sim -1$ which can resolve the LHCb anomalies related with
$B\to K^{(*)} \ell^+ \ell^-$. Therefore both DM and $B$ physics anomalies could
be accommodated in the model.
