A method for solving the inverse quantitative structure-property relationship (QSPR) problem is presented which facilitates the design of novel polymers with targeted properties. Here, we demonstrate the efficacy of the approach using the targeted design of polymers exhibiting a desired glass transition temperature, heat capacity, and density. We present novel QSPRs based on the signature molecular descriptor capable of predicting glass transition temperature, heat capacity, density, molar volume, and cohesive energies of linear homopolymers with cross-validation squared correlation coefficients ranging between 0.81 and 0.95. Using these QSPRs, we show how the inverse problem can be solved to design poly(N-methyl hexamethylene sebacamide) despite the fact that the polymer was used not used in the training of this model.