3D lidar-based simultaneous localization and mapping (SLAM) is a well-recognized solution for mapping and localization applications. However, the typical 3D lidar sensor (e.g., Velodyne HDL-32E) only provides a very limited field of view vertically. As a result, the vertical accuracy of pose estimation suffers. This paper aims to alleviate this problem by detecting the absolute ground plane to constrain vertical pose estimation. Different from the conventional relative plane constraint, this paper employs the absolute plane distance to refine the position in the z-axis and the norm vector of the ground plane to constrain the attitude drift. Finally, relative positioning from lidar odometry, constraint from ground plane detection, and loop closure are integrated under a proposed factor graph-based 3D lidar SLAM framework (AGPC-SLAM). The effectiveness is verified using several data sets collected in Hong Kong.