We use the MultiFractal Detreuded Fluctuation Analysis (MF-I)FA) to study the multifractality of daily return series of Shanghai Stock Exchange (SSE) composite index. There are two main origins of multifractality dynamics of the returns: fat-tailed distributions of Probability Density Function (PDF) and long-range correlations of the series. By analyzing the multifractality singularity spectrum of original, shuffled and surrogated series respectively, we find that both components influence the multifractality in Shanghai stock market and their contributions are almost equal. This phenomena is quite different from the comparing result of NASDAQ composite index, where the multifractality from the fat-tailed probability distributions is dominating.
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