This paper presents a fast and robust plane feature extraction and matching technique for RGB-D type sensors. We propose three algorithm components required to utilize the plane features in an online Simultaneous Localization and Mapping (SLAM) problem: fast plane extraction, frame-to-frame constraint estimation, and plane merging. For the fast plane extraction, we estimate local surface normals and curvatures by a simple spherical model and then segment points using a modified flood fill algorithm. In plane parameter estimation, we suggest a new uncertainty estimation method which is robust against the measurement bias, and also introduce a fast boundary modeling method. We associate the plane features based on both the parameters and the spatial coverage, and estimate the stable constraints by the cost function with a regulation term. Also, our plane merging technique provides a way of generating local maps that are useful for estimating loop closure constraints. We have performed real-world experiments at our lab environment. The results demonstrate the efficiency and robustness of the proposed algorithm.