Contaminated sediment tends to consolidate in response to the loading imposed by an overlying cap layer. The form of transient solute advection through sediments and caps is consequently changed. Therefore, the contaminant discharge into the overlying water is expected to increase and the effectiveness of the in situ capping system will be strongly affected. In this study, a one-dimensional sediment–cap model coupling consolidation and advection–dispersion equation was established. A simplified model was proposed through the sensitivity analysis, and then a parametric study was conducted. Numerical examples concluded that the absorption, degree of sediment saturation, cap thickness, and sediment depth significantly affect the contaminant discharge from the top of the cap. Therefore, these parameters should be considered carefully during cap design.