The integration of knowledge graphs (KGs) with large language models (LLMs) offers significant potential to improve the retrieval phase of retrieval-augmented generation (RAG) systems. In this study, we propose KG-CQR, a novel framework for Contextual Query Retrieval (CQR) that enhances the retrieval phase by enriching the contextual representation of complex input queries using a corpus-centric KG. Unlike existing methods that primarily address corpus-level context loss, KG-CQR focuses on query enrichment through structured relation representations, extracting and completing relevant KG subgraphs to generate semantically rich query contexts. Comprising subgraph extraction, completion, and contextual generation modules, KG-CQR operates as a model-agnostic pipeline, ensuring scalability across LLMs of varying sizes without additional training. Experimental results on RAGBench and MultiHop-RAG datasets demonstrate KG-CQR's superior performance, achieving a 4-6% improvement in mAP and a 2-3% improvement in Recall@25 over strong baseline models. Furthermore, evaluations on challenging RAG tasks such as multi-hop question answering show that, by incorporating KG-CQR, the performance consistently outperforms the existing baseline in terms of retrieval effectiveness