Polymers are widely used to manufacture many chemical products. Often, polymers are designed by trial-and-error, which is expensive and time-consuming. In this work, a new optimization-based computer-aided polymer design (CAPD) framework with a tailored algorithm is proposed to facilitate the design of polymers with desired properties. Considering the inaccuracy of traditional group contribution methods in polymer property prediction, Molecular Dynamics (MD) is properly integrated into the optimization framework to enhance the reliability, instead of simply validating results. The product needs and target properties of polymers are first identified. Then, the design problem is formulated as a mixed-integer nonlinear programming (MINLP) optimization problem. The objective function is formulated using an analytic hierarchy process model to synthetically consider multiple properties as a linear function. Design variables consist of the design of polymer repeat unit and the number of repeat units (i.e., polymer molecular weight). Constraints on polymer properties and structural feasibility are considered. Afterward, the MINLP problem is solved by a two-phase algorithm. In phase one, the influence of molecular weight on polymer properties is neglected and the relaxed problem is solved to identify promising polymer repeat units. In phase two, molecular dynamics simulation is used to predict the properties of polymers with the identified repeat units in various molecule weights. Meanwhile, specific regression functions are generated to represent the influence of molecular weight. By incorporating the regression functions, the original MINLP problem can be solved to obtain the optimal polymer structure and polymer molecular weight. Finally, a tire polymer design case study is used to illustrate the application of the CAPD approach.