This paper presents RefKG, an innovative framework designed to enhance the effectiveness of large language models (LLMs) in knowledge-intensive tasks such as fact-checking and knowledge graph-based question answering. RefKG utilizes knowledge graphs in a reflective manner, enabling the model to identify and adjust relational pathways, reconstruct relevant information, and engage in logical reasoning based on retrieved data. The framework employs a knowledge-focused, multi-task fine-tuning approach, integrating specialized instructions, and a custom training dataset to optimize LLMs for these tasks. Experimental findings demonstrate that RefKG surpasses existing methods across various benchmarks, highlighting its versatility with different model architectures. This approach is compatible with any open-source LLM, providing a powerful tool for real-time, knowledge-based reasoning in the realms of fact verification and answering complex queries.