In this study, the Mooney-Rivlin material with hyperelastic strain energy was proposed for biomechanical modeling of the lung. We modeled the lung as an inhomogeneous Mooney-Rivlin material with uncoupled deviatoric and volumetric behavior. The proposed method was evaluated on the lungs of eight lung cancer patients. For each patient, the lung was segmented from the 4D-CT images and tetrahedral volume mesh of the lung in phase 50% was created by using the adaptive mesh generation toolkit. The demons deformable registration algorithm was used to extract the displacement vector fields (DVFs). The Jacobian of the deformation gradient was calculated from DVFs, and the lung strain energy function was optimized to improve the tumor center of mass (TCM) motion simulation accuracy between respiratory phase 50% and 0%. The average TCM motion simulation error for the proposed strategy is 1.95 mm for eight patients. We observed 13% improvement in the TCM position prediction compared with the homogeneous Mooney-Rivlin modeling.