A percutaneous oxygenator is used to induce a retrograde perfusion of oxygenated blood in a vein to a compromised organ (e.g., to the brain following a stroke, or to the heart following a heart attack). The oxygenator (10) has an occluding balloon (25) and an oxygenation balloon (20) located upstream from the occluding balloon (25). A plurality of hollow gas-permeable fibers (14) surrounds the oxygenation balloon (20). The oxygenator (10) is inserted into a vein (84) downstream from the compromised organ. An external supply of air/oxygen is connected to create a flow through the fibers (14) and thereby oxygenate blood in the surrounding vein. A retrograde flow of oxygenated blood is induced in the vein to the compromised organ by first inflating the occluding balloon (25) to occlude the vein and then inflating the oxygenation balloon (20). Both balloons (25, 20) are then deflated to permit the normal antegrade flow of blood through the vein. This process of inflation and deflation is periodically repeated at a rate of about 30 to 60 cycles per minute. The percutaneous oxygenator (10) may be equipped with multiple occluding balloons for blocking several branches of the venous system leading from the compromised organ.