The experiment for studying the nonlinear change law of the saturated hydraulic conductivity of municipal solid waste (MSW) was developed based the self-developed experimental instrument, the effect law of filling time and porosity on the nonlinear evolution process of saturated hydraulic conductivity was discussed, the limitations of using Freeze-Carman formula to describe the nonlinear relationship between saturated hydraulic conductivity and porosity was proved, and based on the analysis and fitting of experimental results the nonlinear constitutive models between the saturated hydraulic conductivity and the porosity at different filling time were put forward. The experimental results showed that the saturated hydraulic conductivity presented an exponential type increasing trend with porosity; the self-defined exponential function could describe the nonlinear relationship between saturated hydraulic conductivity and porosity well, and the correlation coefficient were all more than 0.92; and the effects of filling time on saturated hydraulic conductivity were significant, especially when the porosity was larger.