Textual description of a physical location, commonly known as an address, plays an important role in location-based services(LBS) such as on-demand delivery and navigation. However, the prevalence of abnormal addresses, those containing inaccuracies that fail to pinpoint a location, have led to significant costs. Address rewriting has emerged as a solution to rectify these abnormal addresses. Despite the critical need, existing address rewriting methods are limited, typically tailored to correct specific error types, or frequently require retraining to process new address data effectively. In this study, we introduce AddrLLM, an innovative framework for address rewriting that is built upon a retrieval augmented large language model. AddrLLM overcomes aforementioned limitations through a meticulously designed Supervised Fine-Tuning module, an Address-centric Retrieval Augmented Generation module and a Bias-free Objective Alignment module. To the best of our knowledge, this study pioneers the application of LLM-based address rewriting approach to solve the issue of abnormal addresses. Through comprehensive offline testing with real-world data on a national scale and subsequent online deployment, AddrLLM has demonstrated superior performance in integration with existing logistics system. It has significantly decreased the rate of parcel re-routing by approximately 43\%, underscoring its exceptional efficacy in real-world applications.