  In this paper, we consider the Cauchy problem for the generalized KP-II
equation \begin{eqnarray*}
u_{t}-|D_{x}|^{\alpha}u_{x}+\partial_{x}^{-1}\partial_{y}^{2}u+\frac{1}{2}\partial_{x}(u^{2})=0,\alpha\geq4.
\end{eqnarray*} The goal of this paper is two-fold. Firstly, we prove that the
problem is locally well-posed in anisotropic Sobolev spaces
H^{s_{1},\>s_{2}}(\R^{2}) with s_{1}>\frac{1}{4}-\frac{3}{8}\alpha, s_{2}\geq 0
and \alpha\geq4. Secondly, we prove that the problem is globally well-posed in
anisotropic Sobolev spaces H^{s_{1},\>0}(\R^{2}) with
-\frac{(3\alpha-4)^{2}}{28\alpha}<s_{1}\leq0. and \alpha\geq4. Thus, our global
well-posedness result improves the global well-posedness result of Hadac
(Transaction of the American Mathematical Society, 360(2008), 6555-6572.) when
4\leq \alpha\leq6.
