  In this paper, we consider a global wellposed problem for the 3-D
incompressible anisotropic Navier-Stokes equations (\textit{ANS}). In order to
do so, we first introduce the scaling invariant Besov-Sobolev type spaces,
$B^{-1+\frac{2}{p},{1/2}}_{p}$ and $B^{-1+\frac{2}{p},{1/2}}_{p}(T)$, $p\geq2$.
Then, we prove the global wellposedness for (\textit{ANS}) provided the initial
data are sufficient small compared to the horizontal viscosity in some suitable
sense, which is stronger than $B^{-1+\frac{2}{p},{1/2}}_{p}$ norm. In
particular, our results imply the global wellposedness of (\textit{ANS}) with
high oscillatory initial data.
