Large language models (LLMs) are rapidly transforming various domains, including biomedicine and healthcare, and demonstrate remarkable potential from scientific research to new drug discovery. Graph-based retrieval-augmented generation (RAG) systems, as a useful application of LLMs, can improve contextual reasoning through structured entity and relationship identification from long-context knowledge, e.g. biomedical literature. Even though many advantages over naive RAGs, most of graph-based RAGs are computationally intensive, which limits their application to large-scale dataset. To address this issue, we introduce fastbmRAG, an fast graph-based RAG optimized for biomedical literature. Utilizing well organized structure of biomedical papers, fastbmRAG divides the construction of knowledge graph into two stages, first drafting graphs using abstracts; and second, refining them using main texts guided by vector-based entity linking, which minimizes redundancy and computational load. Our evaluations demonstrate that fastbmRAG is over 10x faster than existing graph-RAG tools and achieve superior coverage and accuracy to input knowledge. FastbmRAG provides a fast solution for quickly understanding, summarizing, and answering questions about biomedical literature on a large scale. FastbmRAG is public available in https://github.com/menggf/fastbmRAG.