The Iterative Closest Point (ICP) scheme has been widely used for the registration of surfaces and point clouds.However, when working on depth image sequences where there are large geometric planes with small (or even without) details,existing ICP algorithms are prone to tangential drifting and erroneous rotational estimations due to input device errors.In this paper, we propose a novel ICP algorithm that aims to overcome such drawbacks, and provides significantly stabler registration estimation for simultaneous localization and mapping (SLAM) tasks on RGB-D camera inputs. In our approach,the tangential drifting and the rotational estimation error are reduced by: 1) updating the conventional Euclidean distance term with the local geometry information, and 2) introducing a new camera stabilization term that prevents improper camera movement in the calculation. Our approach is simple, fast, effective, and is readily integratable with previous ICP algorithms. We test our new method with the TUM RGB-D SLAM dataset on state-of-the-art real-time 3D dense reconstruction platforms, i.e., ElasticFusion and Kintinuous. Experiments show that our new strategy outperforms all previous ones on various RGB-D data sequences under different combinations of registration systems and solutions.