The design of microstrip antennas is a complex and time-consuming process, especially the step of searching for the best design parameters. Meanwhile, the performance of microstrip antennas can be improved using metamaterial, which results in a new class of antennas called metamaterial antenna. Several parameters affect the radiation loss and quality factor of this class of antennas, such as the antenna size. Recently, the optimal values of the design parameters of metamaterial antennas can be predicted using machine learning, which presents a better alternative to simulation tools and trialand-error processes. However, the prediction accuracy depends heavily on the quality of the machine learning model. In this paper, and benefiting from the current advances in deep learning, we propose a deep network architecture to predict the bandwidth of metamaterial antenna. Experimental results show that the proposed deep network could accurately predict the optimal values of the antenna bandwidth with a tiny value of mean-square error (MSE). In addition, the proposed model is compared with current competing approaches that are based on support vector machines, multi-layer perceptron, K-nearest neighbors, and ensemble models. The results show that the proposed model is better than the other approaches and can predict antenna bandwidth more accurately.