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In the military and civilian domains, the modulation classification in the communication system is an extremely important technology that needs to be constantly updated and improved. In this paper, we present an automatic modulation classification (AMC) model to do modulation classification in 5 typical types of signal modulation BPSK, QPSK, 8PSK, 16QAM, and 64QAM. The proposed algorithm uses an improved AlexNet with deep residual learning, regularization, global pooling, and PReLU activation function to extract features from constellation diagrams for better recognition performance. Compared with the original AlexNet, support vector machine (SVM), and the traditional maximum likelihood-based cumulant technique, experiment results indicate that the proposed AMC model with the improved AlexNet has achieved very good recognition results, with its robustness, generalization, and high efficiency. We also explore the identifiability and reliability of signal transmission under different SNR conditions for different modulation types.