The long-term seepage characteristics of fluid flow in saturated soil are of significant importance. The Riemann-Liouville (R-L) fractional derivative was adopted to modify classical Darcy"s law (hereinafter referred to as modified seepage model) to describe the evolution of soils’ permeability during the long-term seepage process. Data fitting of experimental results given in published literature show that the modified seepage model could more accurately describe the nonlinear evolution of fluid velocity with time. Moreover, the anomalous permeability coefficient value obtained with the modified seepage model is found to be reasonable. The R-L fractional diffusion equation was derived by integrating the modified seepage model into the one-dimensional Biot consolidation model. The explicit (time domain)-implicit (space domain) difference method was employed to discretized the above equation, and the correctness of the algorithm was verified through numerical example. On this basis, the influence of the modified seepage model parameters on the one-dimensional consolidation process of saturated soil was investigated. The results show that fractional order reflects the degree of soil permeability decay. The higher the fractional order, the lower the soil permeability, which leads to a further decrease in the consolidation rate; Additionally, similar to the permeability coefficient , an increase in the abnormal permeability coefficient also accelerates the consolidation rate of saturated soils. However, it is the permeability coefficient plays the dominant role.