Aromatic heterocyclic polyimides are used extensively in industries for their excellent mechanical properties, high glass transition temperatures (T-g), and so on. A quantitative structure-property relationship (QSPR) model was developed to predict the T-g values with 54 aromatic heterocyclic polyimides by using an artificial neural network (ANN) back-propagation algorithm. Fifty-four aromatic heterocyclic polyimides were randomly divided into a training set (36) and a test set (18). Three molecular descriptors (the connectivity index X1A, the topological descriptor PW3, and the 3D-MoRSE descriptor Mor09e) were selected to produce the mode. Simulated with the final optimum ANN model with 3-3-1 structure, the results show that the predicted T-g values are in good agreement with the experimental ones, with the root mean square errors (RMSEs) of 12.4 K (R = 0.935) and 16.4 K (R = 0.937) for the training set and the test set, respectively. POLYM. ENG. SCI., 50:1547-1557, 2010. (C) 2010 Society of Plastics Engineers