We propose a dense RGBD SLAM system based on 3D Gaussian Splatting that provides metrically accurate pose tracking and visually realistic reconstruction. To this end, we first propose a Gaussian densification strategy based on the rendering loss to map unobserved areas and refine reobserved areas. Second, we introduce extra regularization parameters to alleviate the “forgetting” problem during contiunous mapping, where parameters tend to overfit the latest frame and result in decreasing rendering quality for previous frames. Both mapping and tracking are performed with Gaussian parameters by minimizing re-rendering loss in a differentiable way. Compared to recent neural and concurrently developed Gaussian splatting RGBD SLAM baselines, our method achieves state-of-the-art results on the synthetic dataset Replica and competitive results on the real-world dataset TUM. The code is released on https://github.com/ljjTYJR/HF-SLAM.