Age-related macular degeneration (AMD) is an age-related, persistent, painless eye disease that impairs central vision. The central area (macula) of the retina, located at the back of the eye, sustains damage that is the cause of loss of vision. The early detection of AMD can increase the probability of treatment and prevent vision loss. The AMD can be classified into dry and wet AMD based on the absence of neovascularization. This study introduces a new methodology for the classification of AMD using optical coherence tomography (OCT) retinal images. The proposed methodology is based on three stages. The first stage is the data preparation stage for resizing and normalizing the used images. The second stage is the image processing stage for enhancing the image quality as contrast and resolution these enhancements have been checked by the weighted peak signal-to-noise ratio (WPSNR) methodology. The third stage is the deep feature extraction and classification stage, which consists of two sub-models. The first model is MobileNet V1 which has been used as a deep feature extractor. The second model is LSTM (long short-term memory), fed with deep features to classify the AMD stages. A multi-classification with six separate trials has been employed with the proposed methodology, and compared with other models like DenseNet201 and InceptionV3. The proposed model has been tested on a sample of benchmark data with 4005 grayscale images labeled into three classes. The proposed methodology has achieved an accuracy of 98.85%, a sensitivity of 99.09%, and a specificity of 99.1%. To ensure the effectiveness of the proposed methodology, a comparative analysis has been established with previous approaches in the related field, and the results demonstrated the superiority of the proposed system in AMD multi-classification.