Large Language Models (LLMs) have gained significant traction in various applications, yet their capabilities present risks for both constructive and malicious exploitation. Despite extensive training and fine-tuning efforts aimed at enhancing safety, LLMs remain susceptible to jailbreak attacks. Recently, the emergence of multi-turn attacks has intensified this vulnerability. Unlike single-turn attacks, multi-turn attacks incrementally escalate dialogue complexity, rendering them more challenging to detect and mitigate. In this study, we introduce G-Guard, an innovative attention-aware Graph Neural Network (GNN)-based input classifier specifically designed to defend against multi-turn jailbreak attacks targeting LLMs. G-Guard constructs an entity graph for multi-turn queries, which captures the interrelationships between queries and harmful keywords that present in multi-turn queries. Furthermore, we propose an attention-aware augmentation mechanism that retrieves the most relevant single-turn query based on the ongoing multi-turn conversation. The retrieved query is incorporated as a labeled node within the graph, thereby enhancing the GNN's capacity to classify the current query as harmful or benign. Evaluation results show that G-Guard consistently outperforms all baselines across diverse datasets and evaluation metrics, demonstrating its efficacy as a robust defense mechanism against multi-turn jailbreak attacks.