Addressing non-factoid question answering (NFQA) remains challenging due to its open-ended nature, diverse user intents, and need for multi-aspect reasoning. These characteristics often reveal the limitations of conventional retrieval-augmented generation (RAG) approaches. To overcome these challenges, we propose Typed-RAG, a framework for type-aware decomposition of non-factoid questions (NFQs) within the RAG paradigm. Specifically, Typed-RAG first classifies an NFQ into a predefined type (e.g., Debate, Experience, Comparison). It then decomposes the question into focused sub-queries, each focusing on a single aspect. This decomposition enhances both retrieval relevance and answer quality. By combining the results of these sub-queries, Typed-RAG produces more informative and contextually aligned responses. Additionally, we construct Wiki-NFQA, a benchmark dataset for NFQA covering a wide range of NFQ types. Experiments show that Typed-RAG consistently outperforms existing QA approaches based on LLMs or RAG methods, validating the effectiveness of type-aware decomposition for improving both retrieval quality and answer generation in NFQA. Our code and dataset are available on https://github.com/TeamNLP/Typed-RAG.