Remaining useful life (RUL) prediction is crucial for maintaining modern industrial systems, where equipment reliability and operational safety are paramount. Traditional methods, based on small-scale deep learning or physical/statistical models, often struggle with complex, multidimensional sensor data and varying operating conditions, limiting their generalization capabilities. To address these challenges, this paper introduces an innovative regression framework utilizing large language models (LLMs) for RUL prediction. By leveraging the modeling power of LLMs pre-trained on corpus data, the proposed model can effectively capture complex temporal dependencies and improve prediction accuracy. Extensive experiments on the Turbofan engine's RUL prediction task show that the proposed model surpasses state-of-the-art (SOTA) methods on the challenging FD002 and FD004 subsets and achieves near-SOTA results on the other subsets. Notably, different from previous research, our framework uses the same sliding window length and all sensor signals for all subsets, demonstrating strong consistency and generalization. Moreover, transfer learning experiments reveal that with minimal target domain data for fine-tuning, the model outperforms SOTA methods trained on full target domain data. This research highlights the significant potential of LLMs in industrial signal processing and RUL prediction, offering a forward-looking solution for health management in future intelligent industrial systems.