In recent years, deep learning is an emerging trend with potential applications in ophthalmology. Glaucoma is one ophthalmic disease where early detection is required to avoid vision loss. In the context of deep learning, convolution neural networks (CNN) are preferred for glaucoma classification because they can extract the highly discriminate features effectively from raw pixel intensities. In our approach, the region-of-interest (ROI) can be segmented from the fundus images using variable mode decomposition (VMD) by splitting the coefficients into 5 recurrence decays and upgrading the normal recurrence ranges. This approach will improve the possibility of identifying even poorly differentiated exudates. Later, a 26-layer CNN which involves six convolution layers, four pooling layers, and one fully connected layer that is designed and trained to extract distinctive features from the selective ROI and classified using the softmax layer. Data augmentation technique is employed in our model to enhance the size of dataset and the model is validated using 10-fold cross validation (CV) and 70:30 split ratio approach, and evaluated the performance metrics for different values of batch size, and initial learning rate. The proposed model is verified on a set of balanced and unbalanced public datasets (Drishti-GS1, RIM-ONE and ACRIMA) and the significant accuracy values of the results can be obtained as 90.32% for Drishti-GS1, 90.51% for RIM-ONE, and 96.70% for ACRIMA datasets. To verify the robustness of the model, the proposed model is also validated on two other datasets: (i) a private dataset, and (ii) a huge challenge dataset Refuge. The proposed model given satisfactory results when implemented on these two datasets and the significant accuracy values of the results can be obtained as 88.89% for the private dataset, and 89.17% for Refuge datasetThe obtained results and evaluated performance metrics show that our proposed model classifies the retinal fundus images effectively.