Real-time dense SLAM techniques aim to reconstruct the dense three-dimensional geometry of a scene in real time with an RGB or RGB-D sensor. An indoor scene is an important type of working environment for these techniques. The planar prior can be used in this scenario to improve the reconstruction quality, especially for large low-texture regions that commonly occur in an indoor scene. This article fully explores the planar prior in a dense SLAM pipeline. First, we propose a novel plane detection and segmentation method that runs at 200 Hz on a modern graphics processing unit. Our algorithm for constructing global plane constraints is very efficient; hence, we use it in the process of each input frame for the camera pose estimation while maintaining the real-time performance. Second, we propose herein a plane-based map representation that greatly reduces the memory footprint of plane regions while keeping the geometric details on planes. The experiments reveal that our system yields superior reconstruction results with planar information running at more than 30 fps. Aside from speed and storage improvements, our technique also handles the low-texture problem in plane regions.