  In \cite{YZ}, the author proved the global existence of the two-dimensional
anisotropic quasi-geostrophic equations with condition on the parameters
$\alpha,$ $\beta$ in the Sobolev spaces $H^s( \R^2)$; $s\geq 2$. In this paper,
we show that this equations has a global solution in the spaces $H^s(\R^2)$,
where $\max\{2-2\alpha,2-2\beta\}< s<2$, with additional condition over
$\alpha$ and $\beta$. The proof is based on the Gevrey-class regularity of the
solution in neighborhood of zero.
