Traffic forecasting 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 explainability in traffic prediction models remains a challenge due to the complexity of traffic data and the inherent opacity of deep learning models. To tackle these challenges, we propose a traffic flow prediction model based on large language models (LLMs) to generate explainable traffic predictions, named xTP-LLM. By transferring multi-modal traffic data into natural language descriptions, xTP-LLM captures complex time-series 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, xTP-LLM shows competitive accuracy compared with deep learning baselines, while providing an intuitive and reliable explanation for predictions. This study contributes to advancing explainable traffic prediction models and lays a foundation for future exploration of LLM applications in transportation.