Engineered landfills are designed to protect the soil and groundwater by containing the municipal solid waste disposal sites that prioritize environmental protection. These landfills typically contain the soil and groundwater by containing the municipal solid waste which decomposes and generates leachate. To mitigate these risks, low-permeability landfill liners act as barriers to prevent contaminant transport. However, a few studies have focused on simulating contaminant transport to evaluate the thickness of liner. Therefore, this study investigates the effectiveness of sand–bentonite mixtures as liner materials by simulating contaminant transport using a one-dimensional finite difference method. The model incorporates the coupled process of advection–dispersion–adsorption–diffusion. Furthermore, the study examines the effect of sand gradation (fine sand, medium sand, and coarse sand), and composite sand–bentonite liner thickness on the leaching of contaminants such as chloride, zinc, and lead. The results indicate that reducing the bentonite content from 30 to 10% increases the permeability (3.14 X 10–11 m/s) by 51%, 73%, and 98% for fine, medium, and coarse sand–bentonite mixtures, respectively, leading to higher contaminant concentration at the exit of liner. Conversely, increasing bentonite content enhances contaminant retention by lowering the permeability and increasing cohesion by 1.66, 3.39, and 5.95 times for fine, medium and coarse sand respectively. These findings highlight the importance of optimizing sand–bentonite mixtures to improve the effectiveness of landfill liners.