Automated Program Repair (APR) has emerged as a promising paradigm for reducing debugging time and improving the overall efficiency of software development. Recent advances in Large Language Models (LLMs) have demonstrated their potential for automated bug fixing and other software engineering tasks. Nevertheless, the general-purpose nature of LLM pre-training means these models often lack the capacity to perform project-specific repairs, which require understanding of domain-specific identifiers, code structures, and contextual relationships within a particular codebase. As a result, LLMs may struggle to generate correct patches when the repair depends on project-specific information. To address this limitation, we introduce RelRepair, a novel approach that retrieves relevant project-specific code to enhance automated program repair. RelRepair first identifies relevant function signatures by analyzing function names and code comments within the project. It then conducts deeper code analysis to retrieve code snippets relevant to the repair context. The retrieved relevant information is then incorporated into the LLM's input prompt, guiding the model to generate more accurate and informed patches. We evaluate RelRepair on two widely studied datasets, Defects4J V1.2 and ManySStuBs4J, and compare its performance against several state-of-the-art LLM-based APR approaches. RelRepair successfully repairs 101 bugs in Defects4J V1.2. Furthermore, RelRepair achieves a 17.1\% improvement in the ManySStuBs4J dataset, increasing the overall fix rate to 48.3\%. These results highlight the importance of providing relevant project-specific information to LLMs, shedding light on effective strategies for leveraging LLMs in APR tasks.