Accurate and precise glaucoma screening is crucial for early assessment to prevent blindness, particularly in communities where access to ophthalmologists’ services is limited. It is in this context where convolutional neural networks (CNN) can be harnessed to help in the correct and dependable recognition of glaucoma. One of the neural network parameters that needed to be considered is the issue of batch size. There were very few studies exploring the impact of batch size in the diagnostic capability of neural networks but none so far for glaucoma classification. The purpose of the study is to probe the diagnostic capability of CNN in glaucoma classification as well as to investigate the suitable batch size generating the optimum classification performance of these models. Various CNN models (base CNN, VGG16, ResNet50, and DenseNet121) were applied to a Retinal Image Dataset. The models generated high values for the performance indicators with accuracy (79% - 88%), recall (80% - 93%), precision (79% - 86%) and F1-score (81% - 89%) indicating good and acceptable diagnostic capability for glaucoma recognition. DenseNet121 obtained the highest normalized Matthews Correlation Coefficient stipulating the best diagnostic capability for glaucoma classification. The batch sizes with the best diagnostic capability were 64 and 128 (base CNN model), 64 (VGG16), 16 (ResNet50), and 16 (DenseNet121). The results agreed with the recommendations of other published works of using lower batch size particularly for deeper neural network models as higher batch sizes did not generate superior performance as well posing hardware constraints. The deployment and incorporation of these CNN models can be useful complementary support tools aiding health professionals in the initial assessment of patients. This approach would allow health professionals to initiate referrals to experts for further management thereby preventing visual impairment to our patients. A working partnership of healthcare workers with data scientists is very ideal and helpful for quick and precise diagnosis of glaucoma leading to prevention of blindness in our patients.