The use of hollow-fiber membrane bioreactors (HFMBs) has been proposed for three-dimensional bone tissue growth at the clinical scale. However, to achieve an efficient HFMB design, the relationship between cell growth and environmental conditions must be determined. Therefore, in this work, a dynamic double-porous media model was developed to determine nutrient-dependent cell growth for bone tissue formation in a HFMB. The whole hollow-fiber scaffold within the bioreactor was treated as a porous domain in this model. The domain consisted of two interpenetrating porous regions, including a porous lumen region available for fluid flow and a porous extracapillary space filled with a collagen gel that contained adherent cells for promoting long-term growth into tissue-like mass. The governing equations were solved numerically and the model was validated using previously published experimental results. The contributions of several bioreactor design and process parameters to the performance of the bioreactor were studied. The results demonstrated that the process and design parameters of the HFMB significantly affect nutrient transport and thus cell behavior over a long period of culture. The approach presented here can be applied to any cell type and used to develop tissue engineering hollow-fiber scaffolds.