  We calculate shear viscosity of the quark matter at finite temperature and
density. If we assume that the quark interacts with the soft mode, which is a
collective mode of quark-antiquark pair, the self energy of the quark is
calculated by using the quasi-particle random phase approximation. It is shown
that its imaginary part is large and the mean free path of the quark is short.
With the use of the Kubo formula, the shear viscosity of quark matter becomes
small. The Reynolds number of the quark matter is estimated to be about $3\sim
30$. As the temperature increases, the shear viscosity increases gradually for
$T>200{\rm MeV}$. Moreover it is shown that the shear viscosity is not
sensitive to the chemical potential.
