A transient haemodynamic study in a model cavopulmonary vascular system has been carried out for a typical range of parameters using a finite element-based Navier-Stokes solver. The focus of this study is to investigate the influence of non-Newtonian behaviour of the blood on the haemodynamic quantities, such as wall shear stress (WSS) and flow pattern. The computational fluid dynamics (CFD) model is based on an artificial compressibility characteristic-based split (AC-CBS) scheme, which has been adopted to solve the Navier-Stokes equations in space-time domain. A power law model has been implemented to characterize the shear thinning nature of the blood depending on the local strain rate. Using the computational model, numerical investigations have been performed for Newtonian and non-Newtonian flows for different frequencies and input pulse forms. The haemodynamic quantities observed in total cavopulmonary connection (TCPC) for the above conditions suggest that there are considerable differences in average (about 25-40%) and peak (about 50%) WSS distributions, when the non-Newtonian behaviour of the blood is taken into account. The lower WSS levels observed for non-Newtonian cases point to the higher risk of lesion formation, especially at higher pulsation frequencies. A realistic pulse form is relatively safer than a sinusoidal pulse as it has more energy distributed in the higher harmonics, which results in higher average WSS values. The present study highlights the importance of including non-Newtonian shear thinning behaviour for modelling blood flow in the vicinity of repaired arterial connections. © 2010 John Wiley & Sons, Ltd..