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Firstly, we prove that the Cauchy problem for generalized KP-I equation \\begin{eqnarray*}\n  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\n  \\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 $4\\leq \\alpha \\leq5$. 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