Purpose: Hypoplastic left heart syndrome (HLHS) is a congenital heart disease and is usually associated with pulmonary artery stenosis. The superior vena cava-to-pulmonary artery (bidirectional Glenn) shunt is used primarily as a staging procedure to the total cava-to-pulmonary connection for single-ventricle complex. When HLHS coexists with pulmonary artery stenosis, the surgeons then face a multiple problem. This leads to high demand of optimized structure of Glenn surgery. The objective of this article is to investigate the influence of various anastomotic structures and the direction of superior vena cava (SVC) in Glenn on hemodynamics under pulse inflow conditions and try to find an optimal structure of SVC in Glenn surgery with unilateral pulmonary artery stenosis. Method: First, 3D patient-specific models were constructed from medical images of a HLHS patient before any surgery by using the commercial software Mimics, and another software Free-form was used to deform the reconstructed models in the computer. Four 3D patient-specific Glenn models were constructed: model-1 (normal Glenn), model-2 (lean the SVC back to the stenotic pulmonary artery), model-3 (lean the SVC towards the stenotic pulmonary artery), model-4 (add patch at junction of the SVC toward stenosis at pulmonary artery). Second, a lumped parameter model (LPM) was established to predict boundary conditions for computational fluid dynamics (CFD). In addition, numerical simulations were conducted using CFD through the finite volume method. Finally, hemodynamic parameters were obtained and evaluated. Results: It was showed that model-4 have relatively balanced vena cava blood perfusion into the left pulmonary artery (LPA) and right pulmonary artery (RPA), this may be due to less helical flow and the patch at junction of the SVC. Near stenosis of pulmonary artery, model-4 performed with the higher wall shear stress (WSS), which would benefit endothelial cell function and gene expression. In addition, results showed that model-4 performed with the lower oscillatory shear index (OSI) and wall shear stress gradient (WSSG), which would decrease the opportunity of vascular intimal hyperplasia. Conclusion: It is benefited that surgeons adds patch at junction of the SVC towards stenosis at pulmonary artery. These results can impact the surgical design and planning of the Glenn surgery with unilateral pulmonary artery stenosis.