Retrieval-Augmented Generation (RAG) improves large language models by retrieving external knowledge, often truncated into smaller chunks due to the input context window, which leads to information loss, resulting in response hallucinations and broken reasoning chains. Moreover, traditional RAG retrieves unstructured knowledge, introducing irrelevant details that hinder accurate reasoning. To address these issues, we propose TAdaRAG, a novel RAG framework for on-the-fly task-adaptive knowledge graph construction from external sources. Specifically, we design an intent-driven routing mechanism to a domain-specific extraction template, followed by supervised fine-tuning and a reinforcement learning-based implicit extraction mechanism, ensuring concise, coherent, and non-redundant knowledge integration. Evaluations on six public benchmarks and a real-world business benchmark (NowNewsQA) across three backbone models demonstrate that TAdaRAG outperforms existing methods across diverse domains and long-text tasks, highlighting its strong generalization and practical effectiveness.