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The emergence of Large Language Models (LLMs) has revolutionized many fields, not only traditional natural language processing (NLP) tasks. Recently, research on applying LLMs to the database field has been booming, and as a typical non-relational database, the use of LLMs in graph database research has naturally gained significant attention. Recent efforts have increasingly focused on leveraging LLMs to translate natural language into graph query language (NL2GQL). Although some progress has been made, these methods have clear limitations, such as their reliance on streamlined processes that often overlook the potential of LLMs to autonomously plan and collaborate with other LLMs in tackling complex NL2GQL challenges. To address this gap, we propose NAT-NL2GQL, a novel multi-agent framework for translating natural language to graph query language. Specifically, our framework consists of three synergistic agents: the Preprocessor agent, the Generator agent, and the Refiner agent. The Preprocessor agent manages data processing as context, including tasks such as name entity recognition, query rewriting, path linking, and the extraction of query-related schemas. The Generator agent is a fine-tuned LLM trained on NL-GQL data, responsible for generating corresponding GQL statements based on queries and their related schemas. The Refiner agent is tasked with refining the GQL or context using error information obtained from the GQL execution results. Given the scarcity of high-quality open-source NL2GQL datasets based on nGQL syntax, we developed StockGQL, a dataset constructed from a financial market graph database. It is available at: https://github.com/leonyuancode/StockGQL. Experimental results on the StockGQL and SpCQL datasets reveal that our method significantly outperforms baseline approaches, highlighting its potential for advancing NL2GQL research.