Graph neural networks (GNNs) have exhibited superior performance in various classification tasks on graph-structured data. However, they encounter the potential vulnerability from the link stealing attacks, which can infer the presence of a link between two nodes via measuring the similarity of its incident nodes' prediction vectors produced by a GNN model. Such attacks pose severe security and privacy threats to the training graph used in GNN models. In this work, we propose a novel solution, called Graph Link Disguise (GRID), to defend against link stealing attacks with the formal guarantee of GNN model utility for retaining prediction accuracy. The key idea of GRID is to add carefully crafted noises to the nodes' prediction vectors for disguising adjacent nodes as n-hop indirect neighboring nodes. We take into account the graph topology and select only a subset of nodes (called core nodes) covering all links for adding noises, which can avert the noises offset and have the further advantages of reducing both the distortion loss and the computation cost. Our crafted noises can ensure 1) the noisy prediction vectors of any two adjacent nodes have their similarity level like that of two non-adjacent nodes and 2) the model prediction is unchanged to ensure zero utility loss. Extensive experiments on five datasets are conducted to show the effectiveness of our proposed GRID solution against different representative link-stealing attacks under transductive settings and inductive settings respectively, as well as two influence-based attacks. Meanwhile, it achieves a much better privacy-utility trade-off than existing methods when extended to GNNs.