Abstract: An invariant measure is called a Bernoulli measure if the corresponding dynamics is isomorphic to a Bernoulli shift. We prove that for C^r (r>1) diffeomorphisms any weak-mixing hyperbolic measure could be approximated by Bernoulli measures. This also holds true for C^1 diffeomorphisms preserving a weak-mixing hyperbolic measure with dominated Oseledets splittings.