  The shear viscosity coefficient and the corresponding relaxation time for
causal dissipative hydrodynamics are calculated based on the microscopic
formula proposed in [T. Koide and T. Kodama, Phys. Rev. \textbf{E 78}, 051107
(2008)]. Here, the exact formula is transformed into a more compact form and
applied it to evaluate these transport coefficients in the chiral perturbation
theory and perturbative QCD. It is shown that in the leading order calculation,
the causal shear viscosity coefficient $\eta$ reduces to that of the ordinary
Green-Kubo-Nakano formula, and the relaxation time $\tau_{\pi}$ is related to
$\eta$ and pressure $P$ by a simple relationship, $\tau_{\pi}=\eta/P$.
