3D Gaussian Splatting (3DGS) has gained significant attention for its application in dense Simultaneous Localization and Mapping (SLAM), enabling real-time rendering and high-fidelity mapping. However, existing 3DGS-based SLAM methods often suffer from accumulated tracking errors and map drift, particularly in large-scale environments. To address these issues, we introduce GLC-SLAM, a Gaussian Splatting SLAM system that integrates global optimization of camera poses and scene models. Our approach employs frame-to-model tracking and triggers hierarchical loop closure using a global-to-local strategy to minimize drift accumulation. By dividing the scene into 3D Gaussian submaps, we facilitate efficient map updates following loop corrections in large scenes. Additionally, our uncertainty-minimized keyframe selection strategy prioritizes keyframes observing more valuable 3D Gaussians to enhance submap optimization. Experimental results on various datasets demonstrate that GLC-SLAM achieves superior or competitive tracking and mapping performance compared to state-of-the-art dense RGB-D SLAM systems.