Automatic modulation classification (AMC) is the process of identifying the modulation format of the received signal. It is generally a difficult task due to the limited knowledge of the signal. In this letter, we propose a data driven dictionary-learning-based AMC framework, where we first use the known training signals to train the dictionary set and then classify the unknown modulation format via certain sparse representations, for which we design a dictionary-learning-based algorithm called block coordinate descent dictionary learning. Simulation results show that the proposed method out performs other existing approaches, achieving higher accuracy with a less training time.