Mainstream issue-resolving frameworks predominantly rely on commercial models, leading to high costs and privacy concerns. Existing training approaches for issue resolving struggle with poor generalization and fail to fully leverage open-source development resources. We propose **S**ubtask-**o**riented **R**einforced **F**ine-**T**uning (**SoRFT**), a novel training approach to enhance the issue resolving capability of LLMs. We decomposes issue resolving into structured subtasks: file localization, function localization, line localization, and code edit generation. SoRFT consists of two training stages: (1) **rejection-sampled supervised fine-tuning**, Chain of Thought (CoT) data is filtered using ground-truth before fine-tuning the LLM, and (2) **rule-based reinforcement learning**, which leverages PPO with ground-truth based rewards. We evaluate the SoRFT-trained model on SWE-Bench Verified and SWE-Bench Lite, achieving state-of-the-art (SOTA) performance among open-source models (e.g., resolve 21.4% issues on SWE-Bench Verified with SoRFT-Qwen-7B). The experimental results demonstrate that SoRFT significantly enhances issue-resolving performance, improves model generalization, and provides a cost-efficient alternative to commercial models.