This study investigates rheological effects of blood on steady flows in a nonplanar distal end-to-side anastomosis. The shear-thinning behavior of blood is depicted by a Carreau–Yasuda model and a modified power-law model. To explore effects of nonplanarity in vessel geometry, a curved bypass graft is considered that connects to the host artery with a out-of-plane curvature. Navier–Stokes equations are solved using a finite volume method. Velocity and wall shear stress (WSS) are compared between Newtonian and non-Newtonian fluids at different flow rates. At low flow rate, difference in axial velocity profiles between Newtonian and non-Newtonian fluids is significant and secondary flows are weaker for non-Newtonian fluids. At high flow rate, non-Newtonian fluids have bigger peak WSS and WSS gradient. The size of the flow recirculation zone near the toe is smaller for non-Newtonian fluids and the difference is significant at low flow rate. The nonplanar bypass graft introduces helical flow in the host vessel. Results from the study reveal that near the bed, heel, and toe of the anastomotic junction where intimal hyperplasia occurs preferentially, WSS gradients are all very big. At high flow rates, WSS gradients are elevated by the non-Newtonian effect of blood but they are reduced at low flow rates. At these locations, blood rheology not only affects the WSS and its gradient but also secondary flow patterns and the size of flow recirculation near the toe. This study reemphasizes that the rheological property of blood is a key factor in studying hemodynamic effects on vascular diseases.