The recently developed Neural Radiance Fields (NeRF) and 3D Gaussian Splatting (3DGS) have shown encouraging and impressive results for visual SLAM. However, most representative methods require RGBD sensors and are only available for indoor environments. The robustness of reconstruction in large-scale outdoor scenarios remains unexplored. This paper introduces a large-scale 3DGS-based visual SLAM with stereo cameras, termed LSG-SLAM. The proposed LSG-SLAM employs a multi-modality strategy to estimate prior poses under large view changes. In tracking, we introduce feature-alignment warping constraints to alleviate the adverse effects of appearance similarity in rendering losses. For the scalability of large-scale scenarios, we introduce continuous Gaussian Splatting submaps to tackle unbounded scenes with limited memory. Loops are detected between GS submaps by place recognition and the relative pose between looped keyframes is optimized utilizing rendering and feature warping losses. After the global optimization of camera poses and Gaussian points, a structure refinement module enhances the reconstruction quality. With extensive evaluations on the EuRoc and KITTI datasets, LSG-SLAM achieves superior performance over existing Neural, 3DGS-based, and even traditional approaches. Project page: https://lsg-slam.github.io.