Large strain consolidation theory is applied to calculate deposited cohesive sediment weight deposition and consolidation for the significant nonlinear large strain characteristics. Based on soft soil one-dimensional general large strain consolidation theory and the application of quasi-power functional consolidation constitutive relationships between effective stress, permeability and void ratio, nonlinear large strain consolidation governing equation can be built up according to Darcy law, effective stress principle as well as the soil continuous equation. By the coupling relationship of pore water seepage, element deformation and weight consolidation settlement, a full cohesive sediment weight consolidation numerical model is developed for the nonlinear large strain characteristics. With the fact that deposited sediment weight is as the consolidation loading, the new developed model assumes the deposited sediment layer is homogenous, and the consolidation settlement along with the pore water seepage only occurs in vertical direction, and then the sediment consolidation process can be seen as one dimensional weight consolidation. Moreover, nonlinear quasi-power consolidation constitutive relationship parameters are determined by the cohesive sediment settlement column experiment. Consolidation elements are applied to evaluate the effective stress, excessive pore pressure of different depths, and deposited sediment consolidation settlement is determined by the dissipation of excessive pore pressure in time scale. Numerical model performance shows that there is a clear adjustment process for the relationship of deposited layer effective stress and the void ratio according to the quasi-power functional constitutive relationship in the initial stage. An approximate 20% error between stress and strain consolidation degree means that deposited sediment consolidation settlement develops faster than excessive pore pressure dissipation, which also proves the asynchronous coupling relationship of consolidation deformation and excessive pore pressure dissipation in large strain consolidation. According to the numerical model performances in cohesive sediment consolidation with settlement column experiment, the new developed model outputs show a well agreement with the measured one.