In view of the complexity and high dimensionality of dance action sequence modeling and synthesis, traditional methods are difficult to effectively capture the subtle changes and dynamic coherence between actions. Therefore, this paper introduces a dance action sequence modeling and synthesis method based on deep learning algorithms. First, a convolutional neural network (CNN) is used to extract features from dance videos and extract high-level spatiotemporal features. Then, a long short-term memory (LSTM) network is used to capture the temporal dependency of action sequences, thereby achieving modeling of complex dance action sequences. Finally, a generative adversarial network (GAN) is combined to optimize the quality and naturalness of dance action synthesis. By training the game process between the generator and the discriminator, the realism and fluency of the synthesized action are further improved. Experimental results show that the GAN-based method has a naturalness and fluency score of 4.5 and 4.7, respectively. At the same time, the temporal consistency experiment shows that the change in adjacent frames generated by GAN is always less than 0.1, showing strong temporal continuity and natural transition. From the above data conclusions, the method in this paper can significantly improve the naturalness, fluency and timing consistency of dance movement synthesis, and has strong application potential.