The objective of this study was the fabrication of highly functionalized polymeric three-dimensional (3D) structures characterized by nano and microfibers for use as an extracellular matrix-like tissue engineering scaffold. A hybrid process utilizing direct polymer melt deposition (DPMD) and an electrospinning method were employed to obtain the structure. Each microfibrous layer of the scaffold was built using the DPMD process in accordance with computer-aided design modeling data considering some structural points such as pore size, pore interconnectivity and fiber diameter. Between the layers of the three-dimensional structure, polycaprolactone/collagen nanofiber matrices were deposited via an electrospinning process. To evaluate the fabricated scaffolds, chondrocytes were seeded and cultured within the developed scaffolds for 10 days, and the levels of cell adhesion and proliferation were monitored. The results showed that the polymeric scaffolds with nanofiber matrices fabricated using the proposed hybrid process provided favorable conditions for cell adhesion and proliferation. These conditions can be attributed to enhanced cytocompatibility of the scaffold due to surficial nanotopography in the scaffold, chemical composition by use of a functional biocomposite, and an enlarged inner surface of the structure for cell attachment and growth.