Soil tends to have nonlinear compression characteristics, and the consolidation laws of soil are different under different compression characteristics. Considering the nonlinear characteristics of soil, variable load and continuous drainage boundary conditions, a one-dimensional consolidation equation is established. Its solutions are obtained by using the unconditionally stable finite difference method and semi-analytical method, and the reliability of the two methods is verified by the degradation of continuous drainage boundary condition and the comparison of the two solutions. Based on the solution of finite difference method, the influences of interface parameter, load parameters and nonlinear parameter on soil consolidation are analyzed in detail. The results show that, the larger the interface parameter of continuous drainage boundary, the greater the dissipation rate of excess pore water and the settlement rate of soil, while the interface parameter has no effect on the final settlement. The excess pore water pressure gradually increases at the loading stage and dissipates at the constant loading stage. With the increase of loading rate, both the peak value of excess pore water pressure and soil consolidation rate increase, indicating that extending the construction period is conducive to reducing the influence of excess pore water pressure. It is difficult to accurately predict the consolidation rate of soil in engineering. The accuracy of soil model, boundary conditions and soil calculation parameters should be ensured when the consolidation theory is used.