  We study the Luttinger-liquid parameter $K_{\rho}$ of the Hubbard chain and
the Hubbard ladder models by the ordinary perturbation method combined with the
Luttinger-liquid relation. According to the Luttinger-liquid relation, the
critical exponent $K_{\rho}$ is related to the charge susceptibility $\chi_c$
and the Drude weight D by $ K\sb{\rho}={1/2}(\pi \chi_c D)^{1/2}$. By
calculating these quantities with the perturbation method, we obtain $K_{\rho}$
at the first-order analytically and up to the second-order numerically. We
compare these results with results of the Bethe ansatz for the Hubbard chain
and that of the numerical diagonalization for the Hubbard ladder. It shows that
the perturbation calculation of $K_{\rho}$ is reliable in the weak coupling
regime.
