Grounding natural language queries in graphical user interfaces (GUIs) presents a challenging task that requires models to comprehend diverse UI elements across various applications and systems, while also accurately predicting the spatial coordinates for the intended operation. To tackle this problem, we propose GMS: Generalist Scanner Meets Specialist Locator, a synergistic coarse-to-fine framework that effectively improves GUI grounding performance. GMS leverages the complementary strengths of general vision-language models (VLMs) and small, task-specific GUI grounding models by assigning them distinct roles within the framework. Specifically, the general VLM acts as a 'Scanner' to identify potential regions of interest, while the fine-tuned grounding model serves as a 'Locator' that outputs precise coordinates within these regions. This design is inspired by how humans perform GUI grounding, where the eyes scan the interface and the brain focuses on interpretation and localization. Our whole framework consists of five stages and incorporates hierarchical search with cross-modal communication to achieve promising prediction results. Experimental results on the ScreenSpot-Pro dataset show that while the 'Scanner' and 'Locator' models achieve only $2.0\%$ and $3.7\%$ accuracy respectively when used independently, their integration within GMS framework yields an overall accuracy of $35.7\%$, representing a $10 \times$ improvement. Additionally, GMS significantly outperforms other strong baselines under various settings, demonstrating its robustness and potential for general-purpose GUI grounding.