Abstract: This work proposes a real-time 6 Degree-of-Freedom (6 DoF) tracking algorithm for monocular laparoscopic surgery. It provides alignment between intra-operative video and pre-operative data (e.g., CT). The 6 DoF tracking offers a solution for accurately locating the internal anatomy of the target organ despite the lack of tactile feedback and transparency. The ORB-SLAM2 framework is adopted and modified for prior-based 3D tracking with four major modifications. First, the primitive 3D shape is used for fast initialization of the ORB-SLAM2 monocular mode. Second, a pseudo-segmentation strategy is employed to separate the target organ from the background for tracking. Third, the 3D shape is incorporated as a geometric prior in its pose graph optimization. Fourth, the Multi-Scale Retinex with Chromaticity Preservation (MSRCP) algorithm is leveraged and modified for image enhancement in challenging illumination scenarios. In-vivo and ex-vivo experiments validate that LapaTrack-3D provides robust 3D tracking and effectively handles typical challenges such as poor illumination, fast motion, out-of-field-of-view scenarios, partial visibility, and ``organ-background'' relative motion. LapaTrack-3D achieves a processing rate of 13 Hz for 1280*720 pixel video.