Regulation of cell-material interactions is an important factor for modulating the cell function in many tissue engineering applications. A more attractive strategy for enhancing the cell-material interactions is to mimic the physical and chemical features of the native extracellular matrix (ECM). The main goal of this study was to develop ECM-like substrates that can control the cell-material interactions including adhesion, spreading, proliferation and differentiation. Poly(L-lactide-co-${varepsilon}$-caprolactone) (PLCL) fibrous meshes were fabricated using electrospinning. The meshes were functionalized with acrylic acid (AAc) using ${gamma}$-ray irradiation, and Arg-Gly-Asp (RGD)-containing peptide was immobilized on the resulting mesh as a cell adhesive ligand. The adhesion and proliferation of the MC3T3-E1 pre-osteoblastic cells grown on the RGD-AAc-PLCL fibrous meshes were greater than those of the cells grown on the other fibrous meshes for up to 7 days. In addition, mature formation of F-actin stress fibers and focal adhesion (co-localized with vinculin) was only observed on the RGD-AAc-PLCL meshes. Moreover, the ALP activity and calcium content on the RGD-AAc-PLCL meshes were approximately 7.5 and 6.7 times higher than those on the other meshes, respectively. In addition, the expression of selected osteogenic genes, Cbfa1, ALP, and OCN, was significantly up-regulated (at least 5 to 9.7 times greater) on the RGD-AAc-PLCL meshes. This suggests that peptide-modified fibrous meshes eliciting desirable cellular responses may provide a useful tool for many tissue engineering applications.