The paper introduces ExKG-LLM, a framework designed to automate the expansion of cognitive neuroscience knowledge graphs (CNKG) using large language models (LLMs). It addresses limitations in existing tools by enhancing accuracy, completeness, and usefulness in CNKG. The framework leverages a large dataset of scientific papers and clinical reports, applying state-of-the-art LLMs to extract, optimize, and integrate new entities and relationships. Evaluation metrics include precision, recall, and graph density. Results show significant improvements: precision (0.80, +6.67%), recall (0.81, +15.71%), F1 score (0.805, +11.81%), and increased edge nodes (21.13% and 31.92%). Graph density slightly decreased, reflecting a broader but more fragmented structure. Engagement rates rose by 20%, while CNKG diameter increased to 15, indicating a more distributed structure. Time complexity improved to O(n log n), but space complexity rose to O(n2), indicating higher memory usage. ExKG-LLM demonstrates potential for enhancing knowledge generation, semantic search, and clinical decision-making in cognitive neuroscience, adaptable to broader scientific fields.