Purpose: Glaucoma is one of the preeminent causes of incurable visual disability and blindness across the world due to elevated intraocular pressure within the eyes. Accurate and timely diagnosis is essential for preventing visual disability. Manual detection of glaucoma is a challenging task that needs expertise and years of experience. Methods: In this paper, we suggest a powerful and accurate algorithm using a convolutional neural network (CNN) for the automatic diagnosis of glaucoma. In this work, 1113 fundus images consisting of 660 normal and 453 glaucomatous images from four databases have been used for the diagnosis of glaucoma. A 13-layer CNN is potently trained from this dataset to mine vital features, and these features are classified into either glaucomatous or normal class during testing. The proposed algorithm is implemented in Google Colab, which made the task straightforward without spending hours installing the environment and supporting libraries. To evaluate the effectiveness of our algorithm, the dataset is divided into 70% for training, 20% for validation, and the remaining 10% utilized for testing. The training images are augmented to 12012 fundus images. Results: Our model with SoftMax classifier achieved an accuracy of 93.86%, sensitivity of 85.42%, specificity of 100%, and precision of 100%. In contrast, the model with the SVM classifier achieved accuracy, sensitivity, specificity, and precision of 95.61, 89.58, 100, and 100%, respectively. Conclusion: These results demonstrate the ability of the deep learning model to identify glaucoma from fundus images and suggest that the proposed system can help ophthalmologists in a fast, accurate, and reliable diagnosis of glaucoma.