The flow conditions representative of physiological states at a distal end-to-side anastomosis of a coronary artery-graft are investigated. Computational fluid dynamic analyses are conducted and the governing equations are 3-D conservation of continuity and momentum equations. The flow is treated as pulsating, isothermal, laminar, Newtonian and incompressible. The cross sectional area ratio and bifurcating angle between the coronary artery and graft are determined to be 1 and 45°, respectively. Two cases of different flow ratios are studied. The flow ratios of graft, artery downstream, and artery upstream are 100:100:0 and 100:80:20. Flow circulation is obvious at the artery upstream throughout the cycle when the flow ratio is 100:80:20. The mean wall shear stress is lower at artery upstream, inner wall of artery downstream, and the stagnation point opposite to the anastomotic junction. High spatial wall shear stress gradient is also observed at these specific locations. Qualitatively speaking, low mean wall shear stress and high spatial wall shear stress gradient are closely related to intimal hyperplasia.