A new stem cell-scaffold construct based on poly-l-lactide (PLLA) nanofibers grafted with collagen (PLLA-COL) and cord blood-derived unrestricted somatic stem cells (USSC) were proposed to hold promising characteristics for bone tissue engineering. Fabricated nanofibers were characterized using SEM, ATR-FTIR, tensile and contact angle measurements. The capacity of PLLA, plasma-treated PLLA (PLLA-pl) and PLLA-COL scaffolds to support proliferation and osteogenic differentiation of USSC was evaluated using MTT assay and common osteogenic markers such as alkaline phosphatase (ALP) activity, calcium mineral deposition and bone-related genes. All three scaffolds showed nanofibrous and porous structure with suitable physical characteristics. Higher proliferation and viability of USSC was observed on PLLA-COL nanofibers compared to control surfaces. In osteogenic medium, ALP activity and calcium deposition exhibited the highest values on PLLA-COL scaffolds on days 7 and 14. These markers were also greater on PLLA and PLLA-pl compared to TCPS. Higher levels of collagen I, osteonectin and bone morphogenetic protein-2 were detected on PLLA-COL compared to PLLA and PLLA-pl. Runx2 and osteocalcin were also expressed continuously on all scaffolds during induction. These observations suggested the enhanced proliferation and osteogenic differentiation of USSC on PLLA-COL nanofiber scaffolds and introduced a new combination of stem cell-scaffold constructs with desired characteristics for application in bone tissue engineering.