If two dissimilar molecules exhibit attraction behavior, then a maximum-boiling azeotrope can be formed. There are very few papers in the open literature studying the design of extractive distillation system for separating of such systems. The design flow sheet of the two-column system is exactly the same as the ones for minimum-boiling azeotrope systems. However, because of different topology of ternary diagram for the maximum boiling system, unique design consideration should be taken to properly design such separation system. A demonstrating example of separating acetone and chloroform via extractive distillation is presented in this paper. A distillation boundary will be formed by adding a heavy entrainer into the system. Depending on the degree of curvature of distillation boundary, feasible minimum entranier-to-feed ratio can be estimated with given product purity specifications. This minimum ratio should be considered as another screening tool for selecting suitable entrainer of maximum-boiling azeotrope systems. An optimal design flow sheet by adding a newly proposed N-methyl-2-pyrrolidone as suitable heavy entrainer is developed for this separation system. Significant savings of total annual cost and energy requirement can be obtained with this newly proposed extractive distillation system as compared to that of the two other published systems in open literatures using either dimethyl sulfoxide or ethylene glycol as entrainer. A simple heat-integration scheme is also proposed to further save energy in this proposed system.