3D Gaussian Splatting (3DGS) has recently gained popularity in SLAM applications due to its fast rendering and high-fidelity representation. However, existing 3DGS-SLAM systems have predominantly focused on indoor environments and relied on active depth sensors, leaving a gap for large-scale outdoor applications. We present BGS-SLAM, the first binocular 3D Gaussian Splatting SLAM system designed for outdoor scenarios. Our approach uses only RGB stereo pairs without requiring LiDAR or active sensors. BGS-SLAM leverages depth estimates from pre-trained deep stereo networks to guide 3D Gaussian optimization with a multi-loss strategy enhancing both geometric consistency and visual quality. Experiments on multiple datasets demonstrate that BGS-SLAM achieves superior tracking accuracy and mapping performance compared to other 3DGS-based solutions in complex outdoor environments.