The growing population of failing single-ventricle (SV) patients might benefit from ventricular assist device (VAD) support as a bridge to heart transplantation. However, the documented experience is limited to isolated case reports. Considering the complex and different physiopathology of Norwood, Glenn, and Fontan patients and the lack of established experience, the aim of this work is to realize and test a lumped parameter model of the cardiovascular system able to simulate SV hemodynamics and VAD implantation effects to support clinical decision. Hemodynamic and echocardiographic data of 30 SV patients (10 Norwood, 10 Glenn, and 10 Fontan) were retrospectively collected and used to simulate patients' baseline. Then, the effects of VAD implantation were simulated. Simulation results suggest that the implantation of VAD: (i) increases the cardiac output and the mean arterial systemic pressure in all the three palliation conditions (Norwood 77.2 and 19.7%, Glenn 38.6 and 32.2%, and Fontan 17.2 and 14.2%); (ii) decreases the SV external work (Norwood 55%, Glenn 35.6%, and Fontan 41%); (iii) decreases the pressure pulsatility index (Norwood 65.2%, Glenn 81.3%, and Fontan 64.8%); (iv) increases the pulmonary arterial pressure in particular in the Norwood circulation (Norwood 39.7%, Glenn 12.1% and Fontan 3%); and (v) decreases the atrial pressure (Norwood 2%, Glenn 10.6%, and Fontan 8.6%). Finally, the VAD work is lower in the Norwood circulation (30.4 mL·mm Hg) in comparison with Fontan (40.3 mL·mm Hg) and to Glenn (64.5 mL·mm Hg) circulations. The use of VAD in SV physiology could be helpful to bridge patients to heart transplantations by increasing the CO and unloading the SV with a decrement of the atrial pressure and the SV external work. The regulation of the pulmonary flow is challenging because the Pap is increased by the presence of VAD. The hemodynamic changes are different in the different SV palliation step. The use of numerical models could be helpful to support patient and VAD selection to optimize the clinical outcome.