Acellular biodegradable small diameter vascular grafts (SDVGs) require antithrombosis, intimal hyperplasia inhibition and rapid endothelialization to improve the graft patency. However, current antithrombosis and antiproliferation approaches often conflict with endothelial cell layer formation on SDVGs. To address this limitation, biodegradable elastic polyurethane urea (BPU) and the drug dipyridamole (DPA) were mixed and then electrospun into a biodegradable fibrous scaffold. The BPU would provide the appropriate mechanical support, while the DPA in the scaffold would offer biofunctions as required above. We found that the resulting scaffolds had tensile strengths and strains comparable with human coronary artery. The DPA in the scaffolds was continuously released up to 91 days in phosphate buffer solution at 37 °C, with a low burst release within the first 3 days. Compared to BPU alone, improved non-thrombogenicity of the DPA-loaded BPU scaffolds was evidenced with extended human blood clotting time, lower TAT complex concentration, lower hemolysis and reduced human platelet deposition. The scaffolds with a higher DPA content (5 and 10%) inhibited proliferation of human aortic smooth muscle cell significantly. Furthermore, the DPA-loaded scaffolds had no adverse effect on human aortic endothelial cell growth, yet it improved their proliferation. The attractive mechanical properties and biofunctions of the DPA-loaded BPU scaffold indicate its potential as an acellular biodegradable SDVG for vascular replacement.