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This paper presents a sliding window multifractal detrending moving average (MF-DMA) method for multifractal analysis of time series. Numerical experiments on the binomial multifractal measure show improvements in fitting theoretical values by sliding window MF-DMA method compared with the original MF-DMA algorithm. We try to assess the multifractality displayed by realized volatility series of SSEC (Shanghai (securities) composite index) and SZSEC (Compositional Index of Shenzhen Stock Market) indexes in Chinese stock market via sliding window MF-DMA method, and the scaling exponents obtained are fitted to a Log-normal multifractal model. Empirical analysis shows clear evidences of the existences of multifractal features in realized volatility series of SSEC and SZSEC indexes, the multifractality degree of SSEC index is stronger than that of SZSEC index. The major sources of multifractality exhibited in realized volatility series of both SSEC and SZSEC indexes are long-range correlations of small and large fluctuations, and the fat-tailed distributions have certain effects on multifractality. The Log-normal multifractal model shows great availability to capture the scaling behavior of realized volatility series of real financial data. [ABSTRACT FROM AUTHOR]