The new era of biomaterials for repairing bone tissue injury continues to be a challenge in bone tissue engineering. The fiber scaffolds allow for cellular interconnection and a microenvironment close to the bone extracellular matrix. The aim of this study was to evaluate the osteoblast behavior on a 3D textile of PGA (polyglycolic acid) fibers functionalized with the RGD (R: arginine; G: glycine; D: aspartic acid) peptide. The cell morphology, proliferation, and calcium phosphate deposition ability were evaluated on textiles at different time intervals under a confocal laser scanning microscope. The osteoblast viability ranged from 92% to 98%, and cell proliferation was higher in PGA-RGD than control PGA (uncoated). In addition, the osteoblast calcium phosphate deposition was significantly greater on PGA-RGD in osteogenic inductor medium (OIM) in contrast to controls without inducing factors. The PGA-RGD fibers supported proliferation and viability of osteoblast and stimulated bone osteogenesis and mineralization. These results support the adoption of this 3D polymeric textile as a scaffold for bone tissue engineering.