Self-supervised learning (SSL) has shown great potential in learning generalizable representations for graph-structured data. However, existing SSL-based graph pre-training methods largely focus on improving graph representations by learning the structure information based on disturbing or reconstructing graphs, which ignores an important issue: the importance of different nodes in the graph structure may vary. To fill this gap, we propose a Centrality-guided Graph Pre-training (CenPre) framework to integrate the distinct importance of nodes in graph structure into the corresponding representations of nodes based on the centrality in graph theory. In this way, the different roles played by different nodes can be effectively leveraged when learning graph structure. The proposed CenPre contains three modules for node representation pre-training and alignment. The node-level importance learning module fuses the fine-grained node importance into node representation based on degree centrality, allowing the aggregation of node representations with equal/similar importance. The graph-level importance learning module characterizes the importance between all nodes in the graph based on eigenvector centrality, enabling the exploitation of graph-level structure similarities/differences when learning node representation. Finally, a representation alignment module aligns the pre-trained node representation using the original one, essentially allowing graph representations to learn structural information without losing their original semantic information, thereby leading to better graph representations. Extensive experiments on a series of real-world datasets demonstrate that the proposed CenPre outperforms the state-of-the-art baselines in the tasks of node classification, link prediction, and graph classification.