The helically distributed ribbons of thrombus, formed in the commercially available SwirlGraft (Veryan Medical, London, UK), are the result of its wall shear stress distribution, which has zonary areas of low wall shear stress. In order to overcome the inherent deficiency of the SwirlGraft, a new helical graft with a noncircular cross section was proposed and compared numerically with the SwirlGraft in terms of wall shear stress distribution, helicity of the swirling flow created, and pressure drop over the grafts. The numerical results showed that due to the modification to the geometrical configuration of the SwirlGraft, wall shear stress in the new helical graft model was enhanced, and the zones of low wall shear stress existing in the SwirlGraft were completely eliminated. The present numerical study also predicted a slightly steeper pressure drop and reduction in helicity in the new helical graft model in comparison with the SwirlGraft model. Based on the study, we believe that the new helical graft with a noncircular cross section may reduce the possibility of acute thrombus formation in the graft because the enhanced wall shear stress can impede the stay and adherence of platelets and leukocytes to the surface of the graft.