Glaucoma is characterized by increased intraocular pressure and damage to the optic nerve, which may result in irreversible blindness. The drastic effects of this disease can be avoided if it is detected at an early stage. However, the condition is frequently detected at an advanced stage in the elderly population. Therefore, early-stage detection may save patients from irreversible vision loss. The manual assessment of glaucoma by ophthalmologists includes various skill-oriented, costly, and time-consuming methods. Several techniques are in experimental stages to detect early-stage glaucoma, but a definite diagnostic technique remains elusive. We present an automatic method based on deep learning that can detect early-stage glaucoma with very high accuracy. The detection technique involves the identification of patterns from the retinal images that are often overlooked by clinicians. The proposed approach uses the gray channels of fundus images and applies the data augmentation technique to create a large dataset of versatile fundus images to train the convolutional neural network model. Using the ResNet-50 architecture, the proposed approach achieved excellent results for detecting glaucoma on the G1020, RIM-ONE, ORIGA, and DRISHTI-GS datasets. We obtained a detection accuracy of 98.48%, a sensitivity of 99.30%, a specificity of 96.52%, an AUC of 97%, and an F1-score of 98% by using the proposed model on the G1020 dataset. The proposed model may help clinicians to diagnose early-stage glaucoma with very high accuracy for timely interventions.