A porous shape memory scaffold with biomimetic architecture is highly promising for bone tissue engineering applications. In this study, a series of new shape memory polyurethanes consisting of organic poly( ε -caprolactone) (PCL) segments and inorganic polydimethylsiloxane (PDMS) segments in different ratios (9 : 1, 8 : 2 and 7 : 3) was synthesised. These PCL-PDMS copolymers were further engineered into porous fibrous scaffolds by electrospinning. With different ratios of PCL: PDMS, the fibers showed various fiber diameters, thermal behaviour and mechanical properties. Even after being processed into fibrous structures, these PCL-PDMS copolymers maintained their shape memory properties, and all the fibers exhibited excellent shape recovery ratios of >90% and shape fixity ratios of >92% after 7 thermo-mechanical cycles. Biological assay results corroborated that the fibrous PCL-PDMS scaffolds were biocompatible by promoting osteoblast proliferation, functionally enhanced biomineralization-relevant alkaline phosphatase expression and mineral deposition. Our study demonstrated that the PCL-PDMS fibers with excellent shape memory properties are promising substrates as bioengineered grafts for bone regeneration.