Abstract: In attempting to stuty the problem of earthquake prediction, the law of magnitude and frequency of earthquakes has recently been employed to search for precursors of large earthquakes and to examine the variation with time and space of the b-value. A question arises that in order to comply with the requirements of earthquake prediction, the time length of earthquake data chosen, should be short. As a consequence, the number of earthquakes used will be greatly reduced, giving rise to increased error in the estimation of the b-value.Based on the law, of magnitude and frequency of earthquakes of Gutenberg and Richter, various methods for estimating b-value have been discussed in this paper, namely the maximum likehood estimate, the moment estimate, the simple linear and non-linear least square estimates ect., of which the respective accuracies are given and compared for their adequacy. Included in this paper for reference is an error chart for b-value estimation, computed by the Monte Carlo Method.