Due to the wide existence of unlabeled graph-structured data (e.g. molecular structures), the graph-level clustering has recently attracted increasing attention, whose goal is to divide the input graphs into several disjoint groups. However, the existing methods habitually focus on learning the graphs embeddings with different graph reguralizations, and seldom refer to the obvious differences in data distributions of distinct graph-level datasets. How to characteristically consider multiple graph-level datasets in a general well-designed model without prior knowledge is still challenging. In view of this, we propose a novel Graph Prompt Clustering (GPC) method. Within this model, there are two main modules, i.e., graph model pretraining as well as prompt and finetuning. In the graph model pretraining module, the graph model is pretrained by a selected source graph-level dataset with mutual information maximization and self-supervised clustering regularization. In the prompt and finetuning module, the network parameters of the pretrained graph model are frozen, and a groups of learnable prompt vectors assigned to each graph-level representation are trained for adapting different target graph-level datasets with various data distributions. Experimental results across six benchmark datasets demonstrate the impressive generalization capability and effectiveness of GPC compared with the state-of-the-art methods.