In this study, the support vector machine (SVM), as a novel type of learning machine, for the first time, was used to construct a quantitative structure-property relationship model for the prediction of the glass transition temperatures ($T_g$) of 77 aromatic polyamides and polybenzimidazoles. After 1664 descriptors generation, four descriptors were selected for the SVM model by means of multiple linear regression. The best predictions were obtained with the Gaussian radical basis kernel (C=15, ${varepsilon}$=0.01 and ${gamma}$=0.5). The root mean square (rms) errors for training set, validation set and prediction set are 12.13, 15.58, and 16.22 K, respectively. Comparison to existing models, the SVM model shows better statistical characteristics.