In the process of treating the dredged slurry under vacuum preloading combined with the prefabricated vertical drains (PVDs), a dense “soil column” with low permeability will be formed around the PVD, which results in a poor drainage condition and an unsatisfactory treatment (i.e., the clogging effect). In this study, in order to predict the consolidation behavior of dredged slurry with different initial water contents, the compressibility and permeability of dredged slurry with different initial water contents are investigated. Based on the compression and permeability curves obtained by laboratory tests, the analytical solution to soil consolidation under vacuum preloading is derived. Both the clogging effect and the effect of the initial water content on the initial effective stress are considered. The developed analytical solution is validated through a series of consolidation tests of dredged slurry under vacuum preloading with different initial water contents. It shows that at a given vacuum preloading, the dissipation rate of excess pore water pressure in the dredged slurry decreases as the initial water content increases. The proposed analytical solution presents reliable predictions on the variation of settlement and degree of consolidation with time in the dredged slurry with different initial water contents under vacuum preloading.