  We consider three dimensional incompressible Navier-Stokes equation $(NS)$
with different viscous coefficient in the vertical and horizontal variables. In
particular, when one of these viscous coefficients is large enough compared to
the initial data, we prove the global well-posedness of this system. In fact,
we obtain the existence of a global strong solution to $(NS)$ when the initial
data verify an anisotropic smallness condition which takes into account the
different roles of the horizontal and vertical viscosity.
