Haemodynamics was widely believed to correlate with anastomosis restenosis. Utilizing the haemodynamic parameters as indicator functions, distal anastomosis was redesigned by some researchers so as to improve the long-term graft patency rate. However, there were few studies upon the proximal anastomosis. Therefore, in this study, flow characteristics and distributions of the haemodynamic parameters in proximal anastomosis under physiological flow condition have been investigated numerically for three different grafting angles: namely, 45 degrees forward facing, 45 degrees backward facing, and 90 degrees anastomotic joints. The simulation results showed a flow separation region along the graft inner wall immediately after the heel at peak flow phase and it decreased in size with the grafting angle shifting from 45 degrees forward facing to 45 degrees backward facing. At the same time, a pair of vortex was found in the cross-sectional planes of the 45 degrees backward facing and 90 degrees grafts. In addition, stagnation point was found along the graft outer wall with small shifting during the physiological cycle. High spatial and temporal wall shear stresses gradients (WSSG) were observed around the anastomotic joint. Low time-averaged wall shear stress (WSS) with elevated oscillation shear index (OSI) was found near the middle of anastomosis at the aorta wall and along the graft inner wall respectively, while high time-averaged WSS with low OSI was found at the heel, the toe, and the region downstream of the toe. These regions correlated to early lesion growth. Elevated time-averaged WSSG was found at the same region, where the elevated low-density lipoprotein (LDL) permeability was observed as reported in the literature. The existence of nearly fixed stagnating location, flow separation, vortex, high time-averaged WSS with low OSI, low time-averaged WSS with elevated OSI, and high time-averaged WSSG may lead to graft stenosis. Moreover, the simulation results obtained were consistent with those of experimental measurements. Based on the validated simulation results, the 45 degrees backward-facing graft was found to have the lowest variation range of time-averaged WSS and the lowest segmental average of WSSG among the three models investigated. The 45 degrees backward-facing graft is thus recommended for the bypass operation with expected higher patency rate.