Prefabricated horizontal drain (PHD) assisted by vacuum pressure has been used in practice to accelerate the consolidation process of dredged soft mud. However, very few studies have investigated the large-strain nonlinear consolidation caused by vacuum-assisted PHD. Therefore, based on the piecewise-linear method, this study proposes a one-dimensional consolidation model (called VCS herein) for the soft soil consolidation induced by vacuum-assisted PHD. The proposed VCS model has the capability to consider the large strain, PHD assisted by time-dependent vacuum pressure, soil self-weight, time-dependent surcharge loading and nonlinear changes of the geotechnical parameters and is thus superior to the existing models in the literature. The VCS was validated by comparing with the analytical and semi-analytical solutions reported in the literature. In addition, model test of PHD-vacuum preloading consolidation was designed and performed to further verify the proposed model, and excellent agreement was observed. Based on this model, a parametric study was performed to investigate the effect of several relevant parameters on the vacuum preloading consolidation. Moreover, the differences between PHD-vacuum consolidation and PVD-vacuum radial consolidation were investigated. The results indicate that the initial soil height, vacuum pressure and boundary condition considerably influence the performance of vacuum preloading (e.g., time rate of consolidation and final settlement), whereas the time-dependent vacuum preloading affects only the time rate of the vacuum preloading consolidation and not the final settlement magnitude. For the same soil layer, the final settlement of PHD-vacuum consolidation and PVD-vacuum radial consolidation is relatively close. However, the consolidation rate of PHD-vacuum consolidation is obviously faster than that of PVD-vacuum consolidation.