Accurate human trajectory prediction is crucial for robotics navigation and autonomous driving. Recent research has demonstrated that incorporating goal guidance significantly enhances prediction accuracy by reducing uncertainty and leveraging prior knowledge. Most goal-guided approaches decouple the prediction task into two stages: goal prediction and subsequent trajectory completion based on the predicted goal, which operate at extreme granularities: coarse-grained goal prediction forecasts the overall intention, while fine-grained trajectory completion needs to generate the positions for all future timesteps. The potential utility of intermediate temporal granularity remains largely unexplored, which motivates multi-granularity trajectory modeling. While prior work has shown that multi-granularity representations capture diverse scales of human dynamics and motion patterns, effectively integrating this concept into goal-guided frameworks remains challenging. In this paper, we propose MGTraj, a novel Multi-Granularity goal-guided model for human Trajectory prediction. MGTraj recursively encodes trajectory proposals from coarse to fine granularity levels. At each level, a transformer-based recursive refinement network (RRN) captures features and predicts progressive refinements. Features across different granularities are integrated using a weight-sharing strategy, and velocity prediction is employed as an auxiliary task to further enhance performance. Comprehensive experimental results in EHT/UCY and Stanford Drone Dataset indicate that MGTraj outperforms baseline methods and achieves state-of-the-art performance among goal-guided methods.