The localization behaviour of the anisotropic extended double-exchange model with both diagonal and spin-orientation-dependent off-diagonal disorder is investigated using the transfer-matrix method. The anisotropy is described by different in-plane and inter-plane hopping integrals. By using a mean-field distribution of the spin orientation, the localization length of electrons is calculated as a function of temperature. It is found that the metal-insulator transition temperature t_MIT of the system increases with decreasing degree of anisotropy γ. On the insulating side, the localization length for t close to t_MIT varies as . We also calculate the value of ν for various γ-values. The comparison of the results obtained and the experimental measurements for the layered mixed-valence Mn oxides is discussed.