Gaussian Splatting has garnered widespread attention due to its exceptional performance. Consequently, SLAM systems based on Gaussian Splatting have emerged, leveraging its capabilities for rapid real-time rendering and high-fidelity mapping. However, current Gaussian Splatting SLAM systems usually struggle with large scene representation and lack effective loop closure adjustments and scene generalization capabilities. To address these issues, we introduce NGM-SLAM, the first GS-SLAM system that utilizes neural radiance field submaps for progressive scene expression, effectively integrating the strengths of neural radiance fields and 3D Gaussian Splatting. We have developed neural implicit submaps as supervision and achieve high-quality scene expression and online loop closure adjustments through Gaussian rendering of fused submaps. Our results on multiple real-world scenes and large-scale scene datasets demonstrate that our method can achieve accurate gap filling and high-quality scene expression, supporting both monocular, stereo, and RGB-D inputs, and achieving state-of-the-art scene reconstruction and tracking performance.