The use of horizontal drains assisted by vacuum loading is an effective method for speeding up the consolidation of dredged soil slurry. However, few studies developed models for the large strain consolidation of clayey slurry with prefabricated horizontal drains (PHDs) under self-weight and vacuum loading considering the effects of nonlinear compression and creep. This study introduces a PHD-assisted finite strain consolidation model considering nonlinear compression and limited creep by incorporating an improved elasto-viscoplastic constitutive equation. Firstly, the governing equations for the consolidation of very soft soil with PHDs were derived and solved by the finite-difference method. Subsequently, the proposed consolidation model was verified by comparing the calculations with the finite element solutions, a laboratory model test, and a field trial performed in Hong Kong. Good agreement with the numerical solutions and measured results indicates that the proposed model can capture the consolidation features with PHD combining staged filling and time-dependent vacuum loading. Then, the proposed model was used to estimate a self-weight consolidation test and field test in Japan to show the performance of the proposed model. Finally, parametric studies were conducted to explore the influence of nonlinear compression and creep on the consolidation of soft soil with PHDs.