Accurate ship trajectory prediction is crucial to ensure maritime safety. Most existing ship trajectory predictors face two issues: reliance on post-clustered trajectories and limited interpretability in decision processes. In this research, we address these challenges by proposing an explainable Ship Trajectory Predictor (STPredictor), which is facilitated by strong reasoning capabilities of large language models (LLMs). We reformulate the ship trajectory prediction as a language modeling problem, encoding heterogeneous maritime scenarios as naturallanguage prompts, and employing supervised fine-tuning to design LLMs specifically for the prediction task. Furthermore, we integrate the Chain-of-Thought (CoT) process into the inference pipeline to enhance the transparency and reliability of predictions, and include explanatory requirements in the inference stage to make the decision process align with human instructions. To comprehensively benchmark STPredictor against strong baselines, we construct two large-scale datasets from global Automatic Identification System (AIS) records, including a geospatial-domain dataset and a draught-domain dataset. Extensive experiments based on these datasets demonstrate the superior performance and interpretability of STPredictor in the trajectory prediction task. These findings indicate that LLMs can effectively encode rich interaction information for understanding complex maritime scenarios, thereby laying a solid foundation for reliable and interpretable decisionmaking in maritime safety.