  We construct a scalar dark matter model with $U(1)_{L_\mu-L_\tau}$ symmetry
in which the dark matter interacts with the quark flavours, allowing lepton
non-universal $b \to s \ell \bar{\ell}$ decays. The model can solve $b \to s
\mu \mu$ ($R_{K^{(*)}}$) anomaly and accommodate the relic abundance of dark
matter simultaneously while satisfying the constraints from other low energy
flavour experiments and direct detection experiments of dark matter. The new
fields include vector-like heavy quarks $U$ and $D$, $U(1)_{L_\mu-L_\tau}$
breaking scalar $S$, as well as the dark matter candidate $X_I$ and its heavy
partner $X_R$. To explain both $b \to s \mu \mu$ anomaly and the dark matter,
{\it i)} large mass difference between $X_R$ and $X_I$ is required, {\it ii)}
electroweak scale dark matter and heavy quarks are favoured, {\it iii)} not
only electroweak scale but ${\cal O}(10)$ TeV dark gauge boson $Z'$ and $X_R$
are allowed.
