In recent years, the application of 3D Gaussian splatting technology in simultaneous localization and mapping systems has made it possible to perform high-quality image rendering using explicit 3D Gaussian models, significantly improving the fidelity of environmental reconstruction. However, the existing methods based on 3DGS have problems such as limited tracking accuracy and lack of global consistency in the 3D reconstruction of complex indoor environments. For this purpose, this paper proposes a dense SLAM algorithm based on 3D Gaussian splatting—SNGO-SLAM. This algorithm combines the advantages of both frame-to-model and frame-to-frame tracking methods, and uses surface normal perception to obtain richer geometric information, significantly improving the tracking accuracy. To address the tracking error that occurs over time, the algorithm introduces a loop closure process and optimizes the 3D Gaussian point representation problem, further enhancing the tracking accuracy. In addition, this algorithm also introduces a dual Gaussian pruning strategy, optimizing memory usage and ensuring precise camera tracking. Experiments on the Replica, ScanNet and TUM RGBD datasets show that while maintaining high rendering quality, the absolute root mean square error of the trajectory of this algorithm on the Replica dataset reaches 0.27 cm. Compared with NICE SLAM, Vox-Fusion, Gaussian SLAM and SplaTAM, the tracking accuracy has increased by 74.53%, 91.26%, 12.90% and 28.95% respectively, providing new ideas for SLAM technology.