One-dimensional nonlinear consolidation equations have been established taking into account the effect of structure stress ratio of natural clay and stepped time-dependent construction loading. Crank-Nicolson formula is adopted to solve these equations using the finite difference method. Numerical results are compared to those of linear and nonlinear consolidation taking no account of structure stress. Finally, effects of nonlinear parameter η/c on consolidation are analyzed, which indicates that consolidation rate increases with the decrease of η/c. Numerical results of considering structure stress or not are similar initially. With the development of consolidation, the nonlinear results of not considering the structure stress overestimate the effect of nonlinearity.