Automatic modulation classification (AMC), which plays critical roles in both civilian and military applications, is investigated in this paper through a deep learning approach. A lot of research has been done on feature-based (FB) AM algorithms in particular. Convolutional neural networks (CNN)-based robust AMC approach is developed in this paper to address the difficulty that current FB AMC methods are often intended for a limited set of modulation and lack of generalisation capacity. In total, 11 different modulation types are taken into consideration. Conventional AMCs can be categorized into maximum likelihood (ML)-based (ML-AMC) and feature-based AMC. This paper proposes a robust Convolutional neural network (CNN)-based automatic modulation classification (AMC) technique. The suggested technique can classify the received signals without feature extraction, and it can learn the features from them automatically. A comparison study was done for the proposed CNN-based AMCs with two different optimizers at two different signal-to-noise ratios to select the best one of them based on the performance.