Deep learning (DL) is a new machine learning (ML) methodology that has found successful implementations in many application domains. However, its usage in communications systems has not been well explored. This paper investigates the use of the DL in modulation classification, which is a major task in many communications systems. The DL relies on a massive amount of data and, for research and applications, this can be easily available in communications systems. Furthermore, unlike the ML, the DL has the advantage of not requiring manual feature selections, which significantly reduces the task complexity in modulation classification. In this paper, we use two convolutional neural network (CNN)-based DL models, AlexNet and GoogLeNet. Specifically, we develop several methods to represent modulated signals in data formats with gridlike topologies for the CNN. The impacts of representation on classification performance are also analyzed. In addition, comparisons with traditional cumulant and ML-based algorithms are presented. Experimental results demonstrate the significant performance advantage and application feasibility of the DL-based approach for modulation classification.