Automatic modulation classification is one of the key technologies to ensure communication security and reliability. In a low signal-to-noise ratio (Low-SNR) environment, the automatic modulation classification recognition rate is low and the recognition type is limited. By using the property that the high-order cumulant is equal to zero of zero-mean white Gaussian noise (WGN), the high-order cumulant is introduced to protect the system from WGN in the signal analysis process. Moreover, the deep learning network structure is introduced to complete the characterization of weak features, which  can effectively solve the problem of the limited modulation method. And it can also solve the problem of low recognition rate under Low-SNR. The experimental results show that the classification accuracy of the proposed method is better than the existing methods in the Gaussian channel environment, and it has a higher recognition rate in different channel environments with Low-SNR. And, it makes the model’s time, phase and frequency offset more robust.