Accurate skill extraction from job descriptions is crucial in the hiring process but remains challenging. Named Entity Recognition (NER) is a common approach used to address this issue. With the demonstrated success of large language models (LLMs) in various NLP tasks, including NER, we propose fine-tuning a specialized Skill-LLM and a light weight model to improve the precision and quality of skill extraction. In our study, we evaluated the fine-tuned Skill-LLM and the light weight model using a benchmark dataset and compared its performance against state-of-the-art (SOTA) methods. Our results show that this approach outperforms existing SOTA techniques.