Biomimetic scaffolds have been investigated in vascular tissue engineering for many years. Excellent biodegradable materials are desired as temporary scaffolds to support cell growth and disappear gradually with the progress of guided tissue regeneration. In the present paper, a series of biodegradable copolymers were synthesized and used to prepared micro/nanofibrous scaffolds for vascular tissue engineering. Poly(lactide-co-glycolide-co-3(S)-methyl-morpholine-2,5-dione) [P(LA-co-GA-co-MMD)] copolymers with different L-lactide (LA), glycolide (GA), and 3(S)-methyl-2,5-morpholinedione (MMD) contents were synthesized using stannous octoate as a catalyst. Moreover, the P(LA-co-GA-co-MMD) nanofibrous scaffolds were prepared by electrospinning technology. The morphology of scaffolds was analyzed by scanning electron microscopy (SEM), and the results showed that the fibers are smooth, regular, and randomly oriented with diameters of 700˘100 nm. The weight loss of scaffolds increased significantly with the increasing content of MMD, indicating good biodegradable property of the scaffolds. In addition, the cytocompatibility of electrospun nanofibrous scaffolds was tested by human umbilical vein endothelial cells. It is demonstrated that the cells could attach and proliferate well on P(LA-co-GA-co-MMD) scaffolds and, consequently, form a cell monolayer fully covering on the scaffold surface. Furthermore, the P(LA-co-GA-co-MMD) scaffolds benefit to excellent cell infiltration after subcutaneous implantation. These results indicated that the P(LA-co-GA-co-MMD) nanofibrous scaffolds could be potential candidates for vascular tissue engineering.