Image-based finite element (FE) modeling of human bones has been increasingly applied as a useful tool in biomedical engineering. However, most existing image-based FE models assume isotropic mechanical properties for bones, although bones are typically anisotropic material. In this study, we attempted to construct anisotropic FE models from medical computed tomography (CT) scans by modifying the existing empirical relations of bone elasticity-density. The hypothesis adopted in the study is that bone anisotropy is generated by the variations of bone density and the proposed anisotropic relations should degenerate to the isotropic ones if bone density variation is taken zero. The effect of considering bone anisotropy in FE models was investigated by numerical studies. The obtained numerical results showed that the relative error in the finite element solutions produced respectively by the isotropic and anisotropic FE models can be as large as 50%. We concluded from this preliminary study that the consideration of anisotropy in bone FE models has a significant effect on the accuracy of bone behavior predicted by the FE models. However, well-designed bone tests have to be conducted to validate the anisotropic bone elasticity-density relation proposed in this study.