Weakly-supervised text classification has received much attention in recent years for it can alleviate the heavy burden of annotating massive data.Among them, keyword-driven methods are the mainstream where user-provided keywords are exploited to generate pseudolabels for unlabeled texts.However, existing methods treat keywords independently, thus ignore the correlation among them, which should be useful if properly exploited.In this paper, we propose a novel framework called ClassKG to explore keyword-keyword correlation on keyword graph by GNN.Our framework is an iterative process.In each iteration, we first construct a keyword graph, so the task of assigning pseudo labels is transformed to annotating keyword subgraphs.To improve the annotation quality, we introduce a self-supervised task to pretrain a subgraph annotator, and then finetune it.With the pseudo labels generated by the subgraph annotator, we then train a text classifier to classify the unlabeled texts.Finally, we re-extract keywords from the classified texts.Extensive experiments on both long-text and short-text datasets show that our method substantially outperforms the existing ones.