In view of the nonlinear rheological characteristics of saturated clayey soil, the secondary consolidation coefficient was assumed as a hyperbolic function of the logarithm of time, and a modified secondary consolidation equation was proposed. Based on this idea, the unified hardening (UH) constitutive model was modified. To verify the effectiveness of the modified UH constitutive model, by taking a kind of reconstituted clayey soil in Henan province as an example, a series of one-dimensional rheological oedometer tests with one-way drainage were carried out. Test results illustrate that there was still some pore water pressure to be dissipated in the soil sample, when the primary consolidation determined by the Cassagrande method was completed. Then, the modified UH constitutive model was applied to simulate the measured data obtained at different loading stages, and results show that the model could fit the data well. Finally, in order to further verify the applicability of the model, some oedometer test results reported in the literature were simulated.