Retrieval-augmented generation (RAG) enhances the question answering (QA) abilities of large language models (LLMs) by integrating external knowledge. However, adapting general-purpose RAG systems to specialized fields such as science and medicine poses unique challenges due to distribution shifts and limited access to domain-specific data. To tackle this, we propose SimRAG, a self-training approach that equips LLMs with joint capabilities of question answering and question generation for domain adaptation. Our method first fine-tunes LLMs on instruction-following, question-answering, and search-related data. Then, it prompts LLMs to generate diverse domain-relevant questions from unlabeled corpora, with an additional filtering strategy to retain high-quality synthetic examples. By leveraging these synthetic examples, the LLMs can improve their performance on domain-specific RAG tasks. Experiments on 11 datasets across three different domains verify the efficacy of SimRAG over baselines by 1.2%–8.6%.