Planes and edges are attractive features for simultaneous localization and mapping (SLAM) in indoor environments because they can be reliably extracted and are robust to illumination changes. However, it remains a challenging problem to seamlessly fuse two different kinds of features to avoid degeneracy and accurately estimate the camera motion. In this article, a plane-edge-SLAM system using an RGB-D sensor is developed to address the seamless fusion of planes and edges. Constraint analysis is first performed to obtain a quantitative measure of how the planes constrain the camera motion estimation. Then, using the results of the constraint analysis, an adaptive weighting algorithm is elaborately designed to achieve seamless fusion. Through the fusion of planes and edges, the solution to motion estimation is fully constrained, and the problem remains well-posed in all circumstances. In addition, a probabilistic plane fitting algorithm is proposed to fit a plane model to the noisy 3-D points. By exploiting the error model of the depth sensor, the proposed plane fitting is adaptive to various measurement noises corresponding to different depth measurements. As a result, the estimated plane parameters are more accurate and robust to the points with large uncertainties. Compared with the existing plane fitting methods, the proposed method definitely benefits the performance of motion estimation. The results of extensive experiments on public data sets and in real-world indoor scenes demonstrate that the plane-edge-SLAM system can achieve high accuracy and robustness.