Glaucoma is a chronic progressive eye condition leading to permanent visual loss. An automatic screening system is necessary to detect primary open-angle glaucoma because it is an insidious disease appearing without symptoms or early warning signs. This work introduces an automatic screening technique to diagnose glaucoma using a support vector machine (SVM). Two case studies are investigated: binary-stage and multi-stage classification of glaucoma. First, there is a comparison of the performance of the hard threshold-based approach to the supervised learning approach using an SVM. Image segmentation techniques are performed to detect important features: the actual sizes of the optic cup and optic disc in vertical and horizontal directions. SVMs with a linear kernel function are used to generate the classifier model, and the results show that using threshold-based classification is inadequate to screen glaucoma. In a second case study, an SVM is applied to develop the classification algorithm focused more on the detection of the glaucoma suspect stage, which is an intermediate stage between the healthy and glaucoma stages. A polynomial kernel function is used to implement the classification model. The unbalanced decision tree (UDT) and one-versus-the-rest (OVR) techniques are combined in the models in order to overcome the limitations of an SVM. Finally, the combination of an SVM with both UDT and OVR techniques yields a reliable result with respect to belonging classes at 99.4%.