We suggest an efficient Simultaneous Localization and 3D Polygon Map Building (SLAM) method with Kinect depth sensor for mobile robots in indoor environments. In this method, Kinect depth data is separated into row planes so that scan line segments are on each row plane. After grouping all scan line segments from all row planes into line groups, a set of 3D Scan polygons are fitted from each line group. A map matching algorithm then figures out pairs of scan polygons and existing map polygons in 3D, and localization is performed to record correct pose of the mobile robot. For 3D map-building, each 3D map polygon is created or updated by merging each matched 3D scan polygon, which considers scan and map edges efficiently. The validity of the proposed 3D SLAM algorithm is revealed via experiments.