Although modulation classification based on deep neural network can achieve high Modulation Classification(MC) accuracies, catastrophic forgetting will occur when the neural network model continues to learn new tasks. In this paper, we simulate the dynamic wireless communication environment and focus on breaking the learning paradigm of isolated automatic MC. We innovate a research algorithm for continuous automatic MC. Firstly, a memory for storing representative old task modulation signals is built, which is employed to limit the gradient update direction of new tasks in the continuous learning stage to ensure that the loss of old tasks is also in a downward trend. Secondly, in order to better simulate the dynamic wireless communication environment, we employ the mini-batch gradient algorithm which is more suitable for continuous learning. Finally, the signal in the memory can be replayed to further strengthen the characteristics of the old task signal in the model. Simulation results verify the effectiveness of the method.