Sharpe ratio is extensively used in performance of portfolio. However, it is based on assumption that return follows normal distribution. In other words, when return in asset is not normal distribution, the Sharpe ratio is not meaningful. This research focuses on Generalized Sharpe ratio with different distribution in eight indexes from 2001/12/31 to 2010/12/31. We try to find a suitable levy process to fit our data. Instead of Normal distribution assumption, we use Jump diffusion, Variance Gamma, Normal Inverse Gaussian, Hyperbolic, Generalized Hyperbolic, as our distribution to solve stylized fact like skewness and kurtosis. Compared the difference between standard Sharpe ratio and Generalized Sharpe ratio, we come to these conclusions: first of all, Generalized Hyperbolic is better levy process to fit our eight indexes. Second, Sharpe ratio under GH levy process has low autocorrelation, and it present that modified Sharpe ratio is more elastic. Third, Generalized Sharpe ratio can uncover the strategy that fund manager manipulate Sharpe ratio. At last, Generalized Sharpe ratio have better predict than standard Sharpe ratio. Keywords: Sharpe ratio, Levy process, GH distribution, portfolio, utility function