Due to thrombosis and intimal hyperplasia, small-diameter vascular grafts have poor long-term patency. A combination strategy based on nitric oxide (NO) and anticoagulants has the potential to address those issues. In this study, poly(ethylene terephthalate) (PET) mats were prepared by electrospinning and coated with tannic acid (TA)/copper ion complexes. The chelated copper ions endowed the mats with sustained NO generation by catalytic decomposition of endogenous S-nitrosothiol. Subsequently, zwitterionic carboxybetaine acrylate (CBA) and argatroban (AG) were immobilized on the mats. The introduced AG and CBA had synergistic effects on the improvement of blood compatibility, resulting in reduced platelet adhesion and prolonged blood clotting time. The biocomposite mats selectively promoted the proliferation and migration of human umbilical vein endothelial cells while inhibiting the proliferation and migration of human umbilical arterial smooth muscle cells under physiological conditions. In addition, the prepared mats exhibited antibacterial activity against Escherichia coli and Staphylococcus aureus. Collectively, the prepared mats hold great promise as artificial small-diameter vascular grafts.