In this study, the morphological galaxy classification process was carried out with a hybrid approach. Since the Galaxy classification process may contain detailed information about the universe’s formation, it remains the current research topic. Researchers divided more than 100 billion galaxies into ten different classes. It is not always possible to understand which class the galaxy types belong. However, Artificial Intelligence (AI) can be used for successful classification. There are studies on the automatic classification of galaxies into a small number of classes. As the number of classes increases, the success of the used methods decreases. Based on the literature, the classification using Convolutional Neural Network (CNN) is better. Three meta-heuristic algorithms are used to obtain the optimum architecture of CNN. These are Grey Wolf Optimizer (GWO), Particle Swarm Optimization (PSO) and Artificial Bee Colony (ABC) algorithms. A CNN architecture with nine hidden layers and two full connected layers was used. The number of neurons in the hidden layers and the fully connected layers, the learning coefficient and the batch size values were optimized. The classification accuracy of my model was 85%. The best results were obtained using GWO. Manual optimization of CNN is difficult. It was carried out with the help of the GWO meta-heuristic algorithm.