The frequent virus-like spread of eWOMs on social platforms plays an important role in product or service marketing and brand image maintenance. How to effectively predict the popularity of eWOMs is of great significance for managers to make reasonable decisions. However, due to the limitations of existing methods and the complexity of the eWOM transmission mechanism, predicting eWOM popularity is still a challenging problem. This study proposes an innovative graph convolutional neural network framework (eWOM-GCN) to predict the eWOM's popularity based on its propagation rules in social platforms. This model employs the spatial graph convolution algorithm to unsupervisedly extract the structural features of the eWOM's propagation paths, and combines its temporal features to predict the future popularity. In this study, the model was applied to the real virus-like spread of eWOMs, and the performance of the model was verified through comparative experiments and ablation experiments.