Pre-treatment liver tumor localization remains a challenging task for radiation therapy, mostly due to the limited tumor contrast against normal liver tissues, and the respiration-induced liver tumor motion. Recently, we developed a biomechanical modeling-based, deformation-driven cone-beam CT estimation technique (Bio-CBCT), which achieved substantially improved accuracy on low-contrast liver tumor localization. However, the accuracy of Bio-CBCT is still affected by the limited tissue contrast around the caudal liver boundary, which reduces the accuracy of the boundary condition that is fed into the biomechanical modeling process. In this study, we developed a motion modeling and biomechanical modeling-guided CBCT estimation technique (MM-Bio-CBCT), to further improve the liver tumor localization accuracy by incorporating a motion model into the CBCT estimation process. MM-Bio-CBCT estimates new CBCT images through deforming a prior high-quality CT or CBCT volume. The deformation vector field (DVF) is solved by iteratively matching the digitally-reconstructed-radiographs (DRRs) of the deformed prior image to the acquired 2D cone-beam projections. Using the same solved DVF, the liver tumor volume contoured on the prior image can be transferred onto the new CBCT image for automatic tumor localization. To maximize the accuracy of the solved DVF, MM-Bio-CBCT employs two strategies for additional DVF optimization: (I) prior-knowledge-guided liver boundary motion modeling with motion patterns extracted from a prior 4D imaging set like 4D-CTs/4D-CBCTs, to improve the liver boundary DVF accuracy; and (II) finite-element-analysis-based biomechanical modeling of the liver volume to improve the intra-liver DVF accuracy. We evaluated the accuracy of MM-Bio-CBCT on both the digital extended-cardiac-torso (XCAT) phantom images and real liver patient images. The liver tumor localization accuracy of MM-Bio-CBCT was evaluated and compared with that of the purely intensity-driven 2D-3D deformation technique, the 2D-3D deformation technique with motion modeling, and the Bio-CBCT technique. Metrics including the DICE coefficient and the center-of-mass-error (COME) were assessed for quantitative evaluation. Using limited-view 20 projections for CBCT estimation, the average (± SD) DICE coefficients between the estimated and the 'gold-standard' liver tumors of the XCAT study were 0.57±0.31, 0.78±0.26, 0.83±0.21, and 0.89±0.11 for 2D-3D deformation, 2D-3D deformation with motion modeling, Bio-CBCT and MM-Bio-CBCT techniques, respectively. Using 20 projections for estimation, the patient study yielded average DICE results of 0.63±0.21, 0.73±0.13 and 0.78±0.12, and 0.83±0.09, correspondingly. The MM-Bio-CBCT localized the liver tumor to an average COME of ~2 mm for both the XCAT and the liver patient studies. Compared to Bio-CBCT, MM-Bio-CBCT further improves the accuracy of liver tumor localization. MM-Bio-CBCT can potentially be used towards pre-treatment liver tumor localization and intra-treatment liver tumor location verification to achieve substantial radiotherapy margin reduction.