Scaffolds combining nano- and submicro-fibers closely mimicking extracellular matrix (ECM) have been poorly exploited for in vitro cancer cell culture. Herein, a combined electrospinning and modified in situ biosynthesis method has been developed to fabricate a novel scaffold consisting of bacterial cellulose (BC) nanofibers and electrospun cellulose acetate (CA) submicrofibers to mimic the fibrillar structure of natural ECM. The CA/BC nano/submicrofibrous scaffold was characterized by scanning electron microscopy (SEM), mechanical strength tests, porosity measurements, and cell studies using the MCF-7 breast cancer cells. In addition, the sensitivity of the cancer cells seeded in the CA/BC nano/submicrofibrous scaffold to an anticancer drug was assessed. It was found that the CA/BC scaffold exhibited an interconnected porous structure in which BC nanofibers penetrated into the submicrofibrous CA scaffold. Such sophisticated structure was responsible for the improved mechanical properties of CA/BC scaffold over the ones obtained using a single kind of fibers. More importantly, the CA/BC scaffold showed improved cell adhesion, migration, and proliferation over single BC or CA scaffold. Finally, cells grown on CA/BC scaffold exhibited a greater doxorubicin resistance than those on single CA or BC scaffold. The results suggest that the CA/BC nano/submicrofibrous scaffold has potential for application in in vitro tumor model for the study of cancer progression and drug screening.