Infants born with univentricular heart disease undergo Fontan surgery to establish separate systemic and pulmonary circulations. This surgery results in better blood circulation across a single ventricle that supplies oxygenated blood to the body and passively returns venous blood to the lungs through the total cavopulmonary connection (TCPC). Reducing the pressure drop across the TCPC during Fontan circulation helps in reducing the work load of univentricular heart, and various designs have been proposed for this purpose. The goal of this work is to analyze the effect of placing a porous insert at an appropriate position in the pulmonary artery, on the pressure drop across the TCPC. A 3D computational model of a total TCPC connection provided with a porous insert is developed and solved by finite volume method, under assumptions of steady, laminar, and Newtonian flows. The effects of the porous medium properties—porosity and permeability—across the connection, are analyzed. Compared to the no-porous medium case, TCPC with the porous medium insert exhibits a maximum reduction of 27% in energy loss for the flow range studied. The porous medium used in TCPC connection lowers the energy dissipation by curtailing the flow recirculation zones across the connection. The influences of the diameter of the blood vessel, total cardiac output, and the thickness, permeability, and position of porous media on energy loss are analyzed. The criteria to select the porous medium properties and position for a given Fontan geometry are also determined. Copyright © 2017 John Wiley & Sons, Ltd.