The rescaled range (R/S) analysis, proposed by Hurst, is a new statistical method. Being different from traditional statistical method, R/S analysis can provide the information of maximum fluctuation (range) of statistical parameters. At present paper, several modern instrumental earthquake catalogues in different spatial scale, temporal scale, and with different seismic activity background are studied, and R/S method is used to analyze the variation of range of seismic parameters such as earthquake frequency, and earthquake time interval. For different seismic parameters, the ratio of range to standard deviation - R/S is a power law function of the length of time, and the exponent H of power law is always greater than 0.5. As we know, H=0.5 is the characteristics of all ideal random processes. Our results indicate that earthquake series is not an ideal Poisson process, on the contrary, the earthquake as a phenomenon bears dual characteristics of randomicity and regularity, and the greater H departs from 0.5, the more regularity the time series will show, and vice versa. With time scale changing, one can give the conservative estimate of the fluctuation, which might occur in a relatively long time scale, only by using the limited and known time records. Being different from the traditional statistical method, R / S analysis can provide the information of maximum fluctuation (range) of statistical parameters. At present paper, several modern instrumental earthquake catalogs in different spatial scale, temporal scale, and with different seismic activity background are studied, and R / S method is used to analyze the variation of range of seismic parameters such as earthquake frequency, and earthquake time interval. parameters, the ratio of range to standard deviation - R / S is a power law function of the length of time, and the exponent H of power law is always greater than 0.5. As we know, H = 0.5 is the characteristics of all ideal random processes. Our results indicate that an earthquake series is not an ideal Poisson process, on the contrary, the earthquake as a phenomenon bears dual characteristics of randomicity and regularity, and the gre. ater H departs from 0.5, the more regularity the time series will show, and vice versa. With time scale changing, one can give the conservative estimate of the fluctuation, which might occur in a relatively long time scale, only by using the limited and known time records.