An extracardiac pumping for supplementing the circulation of blood, including the cardiac output, in a patient without any component thereof being connected to the patient's heart, and methods of using same. One embodiment provides a vascular graft that has a first end that is sized and configured to couple to a non-primary blood vessel and a second end that is fluidly coupled to a pump to conduct blood between the pump and the non-primary blood vessel. An outflow conduit is also provided that has a first end sized and configured to be positioned within the same or different blood vessel, whether primary or non-primary, through the vascular graft. The outflow conduit is fluidly coupled to the pump to conduct blood between the pump and the patient. The vascular graft may be connected to the blood vessel subcutaneously to permit application of the extracardiac pumping system in a minimally-invasive procedure.