Sutureless anastomosis devices have been developed to facilitate arterial bypass surgery on the beating heart. However, these devices can significantly alter the hemodynamics at the end-to-side anastomosis and in the host artery, leading to the formation of thrombus or/and intimal hyperplasia (IH). In this study, a numerical analysis was performed on the hemodynamic performance of the Graft Connector (GC), a sutureless anastomosis device, under pulsatile flow conditions. The results showed that blood flow was severely disturbed in the GC model with the formation of vortices and flow stagnation at the bed and the toe, and distal to each of the stent struts, which led to low wall shear stresses and high oscillating shear indices in these regions. This may cause severe IH in the host artery and compromise the performance of the device. Based on the numerical study, suggestions were proposed for the design of the GC to improve its performance.