  The goal of this paper is three-fold. Firstly, we prove that the Cauchy
problem for generalized KP-I equation \begin{eqnarray*}
  u_{t}+|D_{x}|^{\alpha}\partial_{x}u+\partial_{x}^{-1}\partial_{y}^{2}u+\frac{1}{2}\partial_{x}(u^{2})=0,\alpha\geq4
  \end{eqnarray*} is locally well-posed in the anisotropic Sobolev spaces$
H^{s_{1},\>s_{2}}(\R^{2})$ with $s_{1}>-\frac{\alpha-1}{4}$ and $s_{2}\geq 0$.
Secondly, we prove that the problem is globally well-posed in
$H^{s_{1},\>0}(\R^{2})$ with
$s_{1}>-\frac{(\alpha-1)(3\alpha-4)}{4(5\alpha+3)}$ if $4\leq \alpha \leq5$.
Finally, we prove that the problem is globally well-posed in
$H^{s_{1},\>0}(\R^{2})$ with $s_{1}>-\frac{\alpha(3\alpha-4)}{4(5\alpha+4)}$ if
$\alpha>5$. Our result improves the result of Saut and Tzvetkov (J. Math. Pures
Appl. 79(2000), 307-338.) and Li and Xiao (J. Math. Pures Appl. 90(2008),
338-352.).
