In this work, we proposed a novel computer modeling and simulation (CM&S) technique for motion tracking of lung bronchi (or tumors) under respiration using 9 cases of computed tomography (CT)-based patient-specific finite element (FE) models and the Ogden’s hyperelastic constitutive model. In the fabrication of patient-specific FE models for respiratory system, various organs such as mediastinum, diaphragm, and thorax that could affect the lung motions during breathing were considered. In order to describe the nonlinear material/mechanical behavior of human lung tissue (lung parenchyma), the comparative simulation for biaxial tension-compression of lung tissue were carried out using several hyperelastic models, and then, the Ogden’s model was adopted to as the optimal model. Based on the aforementioned FE models and Ogden’s material model, the 9 cases of respiration simulation were carried out from exhalation to inhalation, and the motion of lung bronchi (or tumors) was tracked. In addition, the changes of lung volume, lung cross-sectional area on the axial plane during breathing were calculated. Finally, the simulation results were quantitatively compared to the inhalation/exhalation CT images of 9 objects to validate the proposed technique. The relative errors of the simulation to the clinical data are able to predict the lung lesion motion with an average landmark error: anterior/posterior, 2.67%; right/left, 2.10%; and superior/inferior direction 1.10% error and confirmed to be well matched within the range of 0.20–5.00% of the total average relative error in the lung superior-inferior cross-sectional area. Additionally, the range of volume error was within 1.29–9.23%.