Glaucoma is a chronic eye disease that is a leading cause of irreversible vision loss worldwide. Early and accurate classification of glaucoma is crucial for timely intervention and effective management. In this study, we propose a novel glaucoma classification model named as Deep-GlaucomaNet based on advanced deep learning techniques to achieve high accuracy and reliability. Here, the GoogLeNet model has been employed as a base model. The last four layers of the GoogLeNet were replaced with the customized 15 layers. The augmentation technique has been applied for avoiding overfitting is-sues. The performance of the model is evaluated with two activation functions ReLU and Swish. The proposed model earns better classification accuracy 94.39% on the G1020 dataset and represents its perfection over other existing models.