Graph neural networks (GNNs) have brought revolutionary advancements to the field of link prediction (LP), providing powerful tools for mining potential relationships in graphs. However, existing methods face challenges when dealing with large-scale sparse graphs and the need for a high degree of alignment between different datasets in transfer learning. Besides, although self-supervised methods have achieved remarkable success in many graph tasks, prior research has overlooked the potential of transfer learning to generalize across different graph datasets. To address these limitations, we propose a novel Graph Attention Adaptive Transfer Network (GAATNet). It combines the advantages of pre-training and fine-tuning to capture global node embedding information across datasets of different scales, ensuring efficient knowledge transfer and improved LP performance. To enhance the model's generalization ability and accelerate training, we design two key strategies: 1) Incorporate distant neighbor embeddings as biases in the self-attention module to capture global features. 2) Introduce a lightweight self-adapter module during fine-tuning to improve training efficiency. Comprehensive experiments on seven public datasets demonstrate that GAATNet achieves state-of-the-art performance in LP tasks. This study provides a general and scalable solution for LP tasks to effectively integrate GNNs with transfer learning. The source code and datasets are publicly available at https://github.com/DSI-Lab1/GAATNet