Abstract: In order to research response law of acoustic emission signal in various stages of time series during destruction process of sandstone, the uniaxial compression test of sandstone was carried out. The Hurst exponent and fractal dimension of the acoustic emission counting time series were obtained based on the R/S time series analysis. The results of test and analysis show that the acoustic emission signal has a good correspondence with the internal crack evolution of the sandstone. The time series of the acoustic emission signal of sandstone failure follows the R/S statistical law and fractal law. In the subintervals of the time series, the Hurst exponent is more than 1/2, showing persistent, that is, the resulting acoustic emission signal shows an increasing trend with the increase of time. The fractal dimension has the characteristics of falling-rising-falling and reaches the lowest at the time of sandstone failure. This trend is consistent with the development of micro-cracks in sandstone.