  In this article, we consider the focusing cubic nonlinear Schr\"odinger
equation(NLS) in the exterior domain outside of a convex obstacle in
$\mathbb{R}^3$ with Dirichlet boundary conditions. We revisit the scattering
result below ground state of Killip-Visan-Zhang by utilizing Dodson and
Murphy's argument and the dispersive estimate established by Ivanovici and
Lebeau, which avoids using the concentration compactness. We conquer the
difficulty of the boundary in the focusing case by establishing a local
smoothing effect of the boundary. Based on this effect and the interaction
Morawetz estimates, we prove the solution decays at a large time interval,
which meets the scattering criterions.
