In this study, we synthesized one type of star-shaped polyurethane (SPU) with star-shaped poly(e-caprolactone) (SPCL) containing different arm numbers as soft segment and 4,4'-diphenyl methane diisocyanate (MDI) as well as chain extender 1,4-butylene glycol (BDO) as hard segment. Proton nuclear magnetic resonance (H-1-NMR) confirmed the chemical structure of the material. Differential scanning calorimetry (DSC) and dynamic mechanical analysis (DMA) results indicated that both the melting temperature (T-m) and transition temperature (T-trans) of SPU decreased with the hard segment composition increase. X-ray diffraction (XRD) results demonstrated that the increase of the crystallinity of SPU following the raised arm numbers endowed a high shape fixity of six-arm star-shaped polyurethane (6S-PU) and a wide melting temperature range, which resulted in an excellent triple-shape memory effect of 6S-PU. The in vitro cytotoxicity assay evaluated with osteoblasts through Alamar blue assay demonstrates that this copolymer possessed good cytocompatibility. This material can be potentially used as a new smart material in the field of biomaterials.