  In this paper, we are concerned with the global well-posedness of a
tri-dimensional MHD system with only vertical viscosity in velocity equation
for the large axisymmetric initial data. By making good use of the axisymmetric
structure of flow and the maximal smoothing effect of vertical diffusion, we
show that $\displaystyle\sup_{2\leq
p<\infty}\int_0^t\frac{\|\partial_{z}u(\tau)\|_{L^p}^{2}}{p^{3/4}}\,\mathrm{d}\tau<\infty$.
With this regularity for the vertical first derivative of velocity vector
field, we further establish losing estimates for the anisotropy tri-dimensional
MHD system to get the high regularity of $(u,b)$, which guarantees that
$\int_0^t\|\nabla u(\tau)\|_{L^\infty}\,\mathrm{d}\tau<\infty$. This together
with the classical commutator estimate entails the global regularity of a
smooth solution.
