  For a C^{1+\alpha} diffeomorphism f preserving a hyperbolic ergodic SRB
measure \mu, Katok's remarkable results assert that \mu can be approximated by
a sequence of hyperbolic sets \{\Lambda_n\}_{n\geq1}. In this paper, we prove
the Hausdorff dimension for \Lambda_n on the unstable manifold tends to the
dimension of the unstable manifold. Furthermore, if the stable direction is one
dimension, then the Hausdorff dimension of \mu can be approximated by the
Hausdorff dimension of \Lambda_n. To establish these results, we utilize the
u-Gibbs property of the conditional measure of the equilibrium measure of
-\psi^{s}(\cdot,f^n) and the properties of the uniformly hyperbolic dynamical
systems.
