Abstract: To address image quality degradation caused by beam hardening in cone-beam computed tomography (CBCT) of multi-material objects, this study proposes an empirical polynomial-based beam-hardening correction method based on epipolar consistency conditions. First, the polychromatic projection in the polynomial correction model is represented as a combination of water and bone projections. The water projection is acquired through a water correction method, and then subjected to image reconstruction, segmentation, and forward projection to obtain the bone tissue path length to characterize the bone projection. Consequently, an empirical polynomial correction model is constructed based on the water-corrected projection and bone tissue path length. Subsequently, by combining epipolar consistency conditions with the empirical polynomial correction model, an equality-constrained least-squares problem is formulated. Finally, the Lagrange multiplier method is employed to solve this problem, yielding optimal polynomial correction coefficients to achieve beam-hardening correction. Experimental results demonstrated that the proposed method could effectively suppress cupping and streak artifacts in reconstructed CT images, thereby improving overall image quality.