This study seeks to utilize large language models (LLMs) to forecast the moving ports of fluid antenna (FA). By repositioning the antenna to the locations identified by our proposed model, we intend to address the mobility challenges faced by user equipment (UE). To the best of our knowledge, this paper introduces, for the first time, the application of LLMs in the prediction of FA ports, presenting a novel model termed Port-LLM. The architecture of our model is based on the pre-trained GPT-2 framework. We designed specialized data preprocessing, input embedding, and output projection modules to effectively bridge the disparities between the wireless communication data and the data format utilized by the pre-trained LLM. Simulation results demonstrate that our model exhibits superior predictive performance under different numbers of base station (BS) antennas and varying UE speeds, indicating strong generalization and robustness ability. Furthermore, the spectral efficiency (SE) attained by our model surpasses that achieved by traditional methods in both medium and high-speed mobile environments.