The extracardiac Fontan connection (EFC) is an effective treatment for congenital single ventricle heart defects. Numerous studies have sought to optimize the EFC design. However, the optimal design of EFC remains uncertain. This study aims to examine the influence of bypass angles between the inferior vena cava (IVC) and right pulmonary artery (RPA), and the angles between the IVC and superior vena cava (SVC), on hemodynamics. Furthermore, this study demonstrates a methodology for cardiovascular surgical planning. First, a three-dimensional anatomical geometry was reconstructed from the medical images of a patient with single ventricle heart defects. Second, based on haptic deformations, six computational models were virtually generated. Third, numerical simulations were conducted using computational fluid dynamics through the finite volume method. Finally, hemodynamic parameters were obtained and evaluated. The hemodynamic parameters, including the flow patterns, streamlines, and swirling flow, were obtained. Meanwhile, the energy loss and flow distributions of vena cava blood were calculated. First, the hepatic artery blood distribution to two lungs and the flow ratio of the left pulmonary artery to RPA are sensitive to the angle between the IVC and RPA and not to that between the IVC and SVC. Second, energy dissipation is mainly sensitive to the angle between the IVC and SVC and not to that between the IVC and RPA. Third, an appropriate increase in the angle between the IVC and RPA or that between the IVC and SVC may lead to optimal options. This study is useful for surgeons in evaluating optimal Fontan options.