Traffic flow prediction is crucial for intelligent transportation systems. It has experienced significant advancements thanks to the power of deep learning in capturing latent patterns of traffic data. However, recent deep-learning architectures require intricate model designs and lack an intuitive understanding of the mapping from input data to predicted results. Achieving both accuracy and interpretability in traffic prediction models remains to be a challenge due to the complexity of traffic data and the inherent opacity of deep learning models. To tackle these challenges, we propose a novel approach, Traffic Flow Prediction LLM (TF-LLM), which leverages large language models (LLMs) to generate interpretable traffic flow predictions. By transferring multi-modal traffic data into natural language descriptions, TF-LLM captures complex spatial-temporal patterns and external factors from comprehensive traffic data. The LLM framework is fine-tuned using language-based instructions to align with spatial-temporal traffic flow data. Empirically, TF-LLM shows competitive accuracy compared with deep learning baselines, while providing intuitive and interpretable predictions. We discuss the spatial-temporal and input dependencies for explainable future flow forecasting, showcasing TF-LLM's potential for diverse city prediction tasks. This paper contributes to advancing explainable traffic prediction models and lays a foundation for future exploration of LLM applications in transportation. To the best of our knowledge, this is the first study to use LLM for interpretable prediction of traffic flow.