Efforts to mineralize electrospun hydrophobic polyester scaffold often require prior surface modification such as plasma or alkaline treatment, which may affect the mechanical integrity of the resultant scaffold. Here through rational design we developed a series of polyurethane block copolymers containing poly[(R)-3-hydroxybutyratel (PHB) as hard segment and poly(ethylene glycol) (PEG) as soft segment that could be easily fabricated into mineralizable electrospun scaffold without the need of additional surface treatment. To ensure that the block copolymers do not swell excessively in water, PEG content in the polymers was kept below 50 wt %. To obtain good dry and hydrated state mechanical properties with limited PEG, low-molecular-weight PHB-diol with M-n 1230 and 1790 were used in various molar feed ratios. The macromolecular characteristics of the block copolymers were confirmed by H-1 NMR spectroscopy, gel permeation chromatography (GPC), and thermal gravimetric analyses (TGA). With the incorporation of the hydrophilic PEG segments, the surface and bulk hydrophilicity of the block copolymers were significantly improved. Differential scanning calorimetry (DSC) revealed that the block copolymers had low PHB crystallinity and no PEG crystallinity. This was further confirmed by X-ray diffraction analyses (XRD) in both dry and hydrated states. With short PHB segments and soft PEG coupled together, the block copolymers were no longer brittle. Tensile measurements showed that the block copolymers with higher PEG content or shorter PHB segments were more ductile. Furthermore, their ductility was enhanced in hydrated states with one particular example showing increment in strain at break from 1090 to 1962%. The block copolymers were fabricated into an electrospun fibrous scaffold that was easily mineralized by simple incubation in simulated body fluid. The materials have good potential for bone regeneration application and may be extended to other applications by simply coating them with other biologically active substances.