In this paper, the dynamics seismic activity and fractal structures in magnitude time series of Sarpol-e Zahab earthquakes are investigated. In this case, the dynamics seismic activity is analyzed through the evolution of the scaling parameter so-called Hurst exponent. By estimating the Hurst parameter, we can investigate how the consecutive earthquakes are related. It has been observed that more than one scaling exponent is needed to account for the scaling properties of earthquake time series. Therefore, the influence of different time-scales on the dynamics of earthquakes is measured by decomposing the seismic time series into simple oscillations associated with distinct time-scales. To this end, the empirical mode decomposition (EMD) method was used to estimate the locally long-term persistence signature derived from the Hurst exponent. As a result, the timedependent Hurst exponent, H(t), was estimated and all values of H>0. 5 was obtained, indicating a long-term memory exists in earthquake time series. The main contribution of this paper is estimating H(t) locally for different time-scales and investigating the long-memory behavior exist in the non-stationary multifractal time-series. The time-dependent scaling properties of earthquake time series are associated with the relative weights of the amplitudes at characteristic frequencies. The superiority of the method is the simplicity and the accuracy in estimating the Hurst exponent of earthquakes in each time, without any assumption on the probability distribution of the time series.