Analyzing the spread of malicious information in social networks is crucial for network security. This paper proposes a malicious information propagation model based on Generative Adversarial Network (GAN) and sparse representation to address the challenges posed by the temporal dynamics of malicious information propagation, data sparsity and incompleteness, and the complexity of the propagation space. Firstly, to tackle the dynamics and timeliness of malicious information, the lifecycle of malicious information is divided into time slices. Static and dynamic features within each time slice are extracted and combined into comprehensive user features to construct a propagation space for malicious information. Secondly, to address the issue of missing samples, we utilize GANs for homomorphic compensation of data and integrate an attention mechanism into the GAN to enhance feature learning and improve the handling of missing data. Finally, to manage the complexity of the propagation space, we leverage sparse representation to capture essential characteristics, combining it with Graph Convolutional Networks (GCNs) to develop a Dynamic Sparse Representation based GCN (DSR-GCN) model for predicting user propagation behavior. Experiments show the model effectively captures malicious information propagation trends.