We discuss shear viscosity of the quark matter by using the Kubo formula and the Nambu–Jona–Lasinio model. It is shown that the leading term of 1/N expansion for the shear viscosity is equivalent to the quasi-particle random phase approximation. Using this approximation, we obtain a formula that the shear viscosity is expressed by the quadratic form of the quark spectral function in the chiral symmetric phase. If we assume the Breit–Wigner type for the spectral function, the shear viscosity is evaluated as a function of the imaginary part of the quark self-energy, which is related to the mean-free path of the quark. It is pointed out that the quark matter seems to be a perfect liquid for the mean free path <2 fm.