Extractive distillation is a widely accepted and commercialized process for separating azeotropic mixtures compared to conventional distillation. The search for high-performing solvents, or entrainers, needed in extractive distillation is a challenging task. The heuristic guideline or experiment-based method for the screening of entrainers is usually not very efficient and limited to the existing, well-known solvents. In this contribution, we propose a multistage theoretical framework to design solvents for extractive distillation. A multiobjective optimization-based computer-aided molecular design (MOO-CAMD) method is developed and used to find a list of Pareto-optimal solvents. In the MOO-CAMD method, two important solvent properties (i.e., selectivity and capacity) that determine the extractive distillation efficiency are simultaneously optimized. The next step involves a further screening of the Pareto-optimal solvents by performing rigorous thermodynamic calculation and analysis. Finally, for each of the remaining solvents, the extractive distillation process is optimally designed, and the best candidate showing the highest process performance is ultimately identified. The overall design framework is illustrated through an example of the n-hexane and methanol separation.