SMS spam poses a significant security challenge on a global scale. Traditional spam prevention methods, such as blacklisting known spam senders, have proven insufficient because spammers can easily circumvent these measures by frequently changing their phone numbers. Over the past decade, researchers have explored various machine learning techniques to tackle the issue of SMS spam. While these methods have demonstrated considerable success, they often struggle with the inherent complexity of spam messages, which are typically concise and challenging to analyze. In this study, we propose an alternative solution by leveraging the advancements in large language models (LLMs). Specifically, we fine-tuned a selected LLM to enhance its ability to classify SMS spam effectively. Our experimental evaluation, conducted on a real-world dataset, demonstrates that fine-tuning an LLM offers measurable improvements in classification performance, highlighting the potential of this approach in combating SMS spam.