The estimated parameter and probability density of stable distribution are obtained by its character function and the Fourier transform. At the same time the stable distribution is applied to fit the Shanghai Stocks Exchange Composite index and the model of GARCH-stable is built up which is supposed to obey the stable distribution in its conditional equation. It is observed that the stable distribution is more suitable to describe the distribution of stocks market in China than the normal distribution and thus the capability to forecast the volatility is advanced.