Graph Neural Networks (GNNs) have found widespread application across various domains, encompassing but not limited to social network analysis, recommendation systems, and fraud detection. Meanwhile, training a sophisticated GNN model is an extremely resource-intensive process. Therefore, protecting the intellectual property of GNN model becomes essential. However, limited research has been conducted on the protection of intellectual property for GNNs. Additionally, current few watermarking methods employed in the context of GNNs overlook the potential vulnerabilities posed by evasion attack and fraudulent declaration attack. To fill this gap, in this paper, we propose a novel GNN watermarking method utilizing a bi-level optimization framework to embed an imperceptible and owner-unique watermark into GNNs. The proposed method achieves indistinguishability and uniqueness of the injected watermark, establishing a secure mechanism for intellectual property protection for GNNs. We evaluate our method on two benchmark datasets and three GNN models. The results indicate that our method effectively verifies model ownership with minimal impact on their primary task performance. Furthermore, the method exhibits remarkable resilience against model fine-tuning and pruning attacks, as well as security against evasion attacks and fraudulent ownership claims.