The creation of small-diameter tissue-engineered vascular grafts using biodegradable materials has the potential to change the quality of cardiovascular surgery in the future. The implantation of these tissue-engineered arterial grafts has yet to reach clinical application. One of the reasons for this is thrombus occlusion of the graft in the acute phase. In this paper, we first describe the causes of accelerated thrombus formation and discuss the drugs that are thought to inhibit thrombus formation. We then review the latest research on methods to locally bind the anticoagulant heparin to biodegradable materials and methods to extend the duration of sustained heparin release. We also discuss the results of studies using large animal models and the challenges that need to be overcome for future clinical applications.