Against the background of sustainable development, landfill covers can consist of a range of materials, from clay to geocomposite and polymer composites. Given engineering and environmental requirements, we analyzed the performance and sustainability of four sanitary landfill cover materials, namely clay, HDPE, PVC, and GCL. Within the principles of environmentally sustainable design, we constructed a material selection index based on the performance as well as the economic and environmental impacts of the materials. In addition, using a data envelopment analysis (DEA) model with an analytic hierarchical process (AHP) preference cone, we developed a C2WH model to evaluate the performance of the selected materials. Through the calculation, we found that the comprehensive indexes of the four covering materials were E1 = 0.2600, E2 = 0.5757, E3 = 0.7815, and E4 = 1.0000, respectively. Our results indicated that the investigated materials could be ranked according to performance as follows: GCL > PVC > HDPE > clay. Thus, our results showed that GCL, with the highest efficiency value, was the optimal cover of the investigated materials. The multiobjective decision model developed in our study can be used as a technical reference and offers support for the selection of eco-friendly landfill cover materials.