The development of novel non-steroidal anti-inflammatory drugs (NSAIDs) free of serious side effects remains an attractive area of research. The availability of hundreds of compounds with known inhibitory activity against COX-2, the intended enzyme target of most NSAIDs, provides an excellent opportunity to explore various quantitative structure-activity relationship models and apply them in the binary classification of compounds. In this work, an artificial neural network or neural net (NN) model was constructed on a dataset consisting of 1380 compounds and 184 attributes, i.e., molecular descriptors. A feedforward NN consisting of 63 input nodes, 1 hidden layer with 33 nodes, and trained on 80% of the dataset by a backpropagation algorithm, has learned after 200 training cycles to classify compounds as active or inactive against COX-2. It has excellent predictive performance (accuracy = 93.5%, AUC = 0.97) on the 20% test set. The neural net classified 875 newly designed variants of COX-2 selective inhibitors and 163 structurally related compounds as active against the COX-2 target. The top hits have superior (or at least comparable) binding affinities compared to the control and possess the desirable properties of an oral drug.