Minimally invasive surgery (MIS) remains technically demanding due to the difficulty of tracking hidden critical structures within the moving anatomy of the patient. In this study, we propose a soft tissue deformation tracking augmented reality (AR) navigation pipeline for laparoscopic surgery of the kidneys. The proposed navigation pipeline addresses two main sub-problems: the initial registration and deformation tracking. Our method utilizes preoperative MR or CT data and binocular laparoscopes without any additional interventional hardware. The initial registration is resolved through a probabilistic rigid registration algorithm and elastic compensation based on dense point cloud reconstruction. For deformation tracking, the sparse feature point displacement vector field continuously provides temporal boundary conditions for the biomechanical model. To enhance the accuracy of the displacement vector field, a novel feature points selection strategy based on deep learning is proposed. Moreover, an ex-vivo experimental method for internal structures error assessment is presented. The ex-vivo experiments indicate an external surface reprojection error of 4.07 ± 2.17mm and a maximum mean absolutely error for internal structures of 2.98mm. In-vivo experiments indicate mean absolutely error of 3.28 ± 0.40mm and 1.90±0.24mm, respectively. The combined qualitative and quantitative findings indicated the potential of our AR-assisted navigation system in improving the clinical application of laparoscopic kidney surgery.