Currently, unmanned underwater vehicle (UUV) clusters have demonstrated effectiveness in performing oceanic tasks, with heterogeneity of UUVs becoming a prevalent trend in development. Therefore, selecting appropriate heterogeneous members is essential for achieving efficient and high-quality task execution. To address this issue, this study proposes a UUV cluster cooperative system task assignment method based on graph neural networks (GNN). This method models the UUV cluster as a graphical structure and utilizes a GNN-based approach that combines cluster topology with task requirements, which can learn to predict the optimal UUV cluster for a given task. In addition, this method is scalable and can be applied to different tasks and clusters.