  The shear viscosity to the entropy density ratio $\eta/s$ of the anisotropic
superfluid has been calculated by means of the gauge/gravity duality in the
presence of the {\it dark matter} sector. The {\it dark matter} has been
described by the Yang-Mills field analogous to the one describing visible
matter sector and it is assumed to interact with the visible field with
coupling constant $\alpha$. Close to the superfluid transition temperature
($T_c$) the analytical solution has been given up to the leading order in a
symmetry breaking parameter and the ratio of the gravitational constant and
Yang-Mils coupling. The tensor element of ratio $\eta/s$ remains unaffected by
the {\it dark matter} for the viscosity tensor in the plane perpendicular to
the symmetry breaking direction (here $yz$). The temperature dependence and the
linear correction in $(1-\alpha)$ in the plane containing this direction (here
$xy$) was also revealed. The correction linearly vanishes for temperature
tending to the critical one $T\rightarrow T_c$.
