  We study the one-dimensional Anderson-Hubbard model using the density-matrix
renormalization group method. The influence of disorder on the
Tomonaga-Luttinger liquid behavior is quantitatively discussed. Based on the
finite-size scaling analysis of density-density correlation functions, we find
the following results: i) the charge exponent is significantly reduced by
disorder at low filling and near half filling, ii) the localization length
decays as $\xi \sim \Delta^{-2}$, where $\Delta$ is the disorder strength,
independently of the on-site Coulomb interaction as well as band filling, and
iii) the localization length is strongly suppressed by the on-site Coulomb
interaction near half filling in association with the formation of the Mott
plateaus.
