The aim of this study was to fabricate nanofibrous scaffolds based on blends of a hydroxyl functionalized polyester (poly(hydroxymethylglycolide-co-ε-caprolactone), pHMGCL) and poly(ε-caprolactone) (PCL), loaded with bovine serum albumin (BSA) as a protein stabilizer and vascular endothelial growth factor (VEGF) as a potent angiogenic factor by means of a coaxial electrospinning technique. The scaffolds were characterized by scanning electron microscopy (SEM), fluorescence microscopy (FM), and differential scanning calorimetry (DSC). The scaffolds displayed a uniform fibrous structure with a fiber diameter around 700 nm. The release of BSA from the core of the fibers was studied by high performance liquid chromatography (HPLC), and it was shown that the coaxial scaffolds composed of blends of pHMGCL and PCL exhibited faster release than the comparative PCL scaffolds. VEGF was also incorporated in the core of the scaffolds, and the effect of the released protein on the attachment and proliferation of endothelial cells was investigated. It was shown that the incorporated protein preserved its biological activity and resulted in initial higher numbers of adhered cells. Thus, these bioactive scaffolds based on blends of pHMGCL/PCL loaded with VEGF can be considered as a promising candidate for tissue engineering applications.