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The transport behavior of bed-load in natural rivers shows the nature of anomalous transport(non-Fick)behavior that cannot be properly quantified by using the theory of Ficks law.Continuous time random walk(CTRW)theory through the long tail distribution of the waiting time and jump step can well capture non-Fick transport phenomena.In this study,the waiting time distribution is Mittag-Leffler(M-L)probability distribution,and the jump step distribution is Levy alpha-stable probability.And the Monte Carlo method was used to simulate the model.To verify the effectiveness of the model,we compared the results of the two sets of experiments(continuous source and instantaneous source).