Biocomposite scaffolds were fabricated by incorporation of nanobredigite (n-BD) into the polymer of poly(ε-caprolactone)–poly(ethyleneglycol)–poly(ε-caprolactone) (PCL–PEG–PCL). The results revealed that the addition of n-BD into PCL–PEG–PCL significantly improved water absorption, compressive strength, and degradability of the scaffolds of n-BD/PCL–PEG–PCL composite (n-BPC) compared with PCL–PEG–PCL scaffolds alone. In addition, the proliferation and alkaline phosphatase activity of MG63 cells cultured on n-BPC scaffolds were obviously higher than that cultured on PCL–PEG–PCL scaffolds. Moreover, the results of the histological evaluation from the animal model revealed that the n-BPC scaffolds significantly improved new bone formation compared with the PCL–PEG–PCL scaffolds, indicating good osteogenesis. The n-BPC scaffolds with good biocompatibility could stimulate cell proliferation, differentiation, and bone tissue regeneration and would be an excellent candidate for bone defect repair.