Background: Glaucoma and diabetic retinopathy are the leading causes of blindness due to an irreversible damage to the retina which results in vision loss. Early detection of these diseases through regular screening is especially important to prevent progression. The image of retinal fundus is the main evaluating strategy for the glaucoma and diabetic retinopathy detection. Then, automated eye disease detection is an important application of retinal image analysis. Compared with classical diagnostic techniques, image classification by convolutional neural networks (CNN) have the potential for better cost-effective performance. Methods: In this paper, we propose the use of MATLAB – retrained AlexNet CNN for computerized eye diseases identification, particularly glaucoma and diabetic retinopathy, by employing retinal fundus images. The acquisition of the database was carried out through free access databases and access upon request. A transfer learning technique is used for retraining the AlexNet CNN. Specifically, the model divides the fundus image dataset into training and testing data. Results: As datasets were added by network training, different values were reported for validation accuracy, false positives and false negatives, precision, and recall. Thus, having NetTransfer I with a validation accuracy value of 94.3% for two classes. NetTransfer II with a validation accuracy value of 91.8% for two classes. NetTransfer III with a validation accuracy value of 89.7% for three classes. Net transfer IV with a validation accuracy value of 93.1% for three classes. Finally, NetTransfer V with a validation accuracy value of 92.1% for three classes. Conclusions: Re-training of the AlexNet network proved to be a powerful tool to create disease detection systems having high accuracy values and being able to discern between more than two diseases.