Large Language Models (LLMs) have demonstrated remarkable proficiency across a variety of complex tasks. One significant application of LLMs is in tackling software engineering challenges, particularly in resolving real-world tasks on GitHub by fixing code based on the issues reported by the users. However, many current approaches rely on proprietary LLMs, which limits reproducibility, accessibility, and transparency. The critical components of LLMs for addressing software engineering issues and how their capabilities can be effectively enhanced remain unclear. To address these challenges, we introduce SWE-Fixer, a novel open-source framework designed to effectively and efficiently resolve GitHub issues. SWE-Fixer comprises two essential modules: a code file retrieval module and a code editing module. The retrieval module employs BM25 along with a lightweight model to achieve coarse-to-fine file retrieval. Subsequently, the code editing module utilizes the other model to generate patches for the identified files. Then, to mitigate the lack of publicly available datasets, we compile an extensive dataset that includes 110K GitHub issues along with their corresponding patches and train the two models of SWE-Fixer separately. We assess our approach on the SWE-Bench Lite and Verified benchmarks, achieving state-of-the-art performance among open-source models with scores of 24.7\% and 32.8\%, respectively.Additionally, our approach requires only two model calls per instance, making it significantly more efficient than existing methods. These results highlight the effectiveness of SWE-Fixer in real-world code-fixing scenarios.Our model, dataset, and code will be released.