The quantitative structure-property relationship (QSPR) was studied for the prediction of glass transition temperatures of polystyrenes on a set of 107 polystyrenes using artificial neural networks combined with genetic function approximation. Descriptors of the polymers were derived from their corresponding cyclic dimer structures. A nonlinear model with four descriptors was developed with squared correlation coefficient ($R^2$) of 0.955 and standard error of estimation (s) of 11.2 K for the training set of 96 polystyrenes. The model obtained was further validated with Leave-One-Out cross-validation and the external test set. The cross-validated correlation coefficient ${R^2}_{CV}$=0.953 illustrates that there seems no chance correlation to happen. The mean relative error (MRE) for the whole data set was 2.3 %, indicating the reliability of the present model to estimate the glass transition temperatures for polystyrenes. The results demonstrate the powerful ability of the cyclic dimer structures as representative of polymers, which could be further applied in QSPR studies on polymers.