Let \(M\) be a compact connected oriented three-dimensional manifold and let \(f:M \to M\) be an expansive diffeomorphism such that \(\Omega (f)=M\). The author proves that if there exists a hyperbolic periodic point with a homoclinic intersection then \(f\) is conjugate to an Anosov isomorphism of \(T^3\). It is also shown that at any homoclinic hyperbolic point, the stable and unstable manifolds of the periodic point must be topologically transitive. The author also conjectures that the existence of the hyperbolic periodic point with a homoclinic intersection is not a necessary condition for \(f\) to be conjugate to the Anosov isomorphism.