An intravenous fiber membrane oxygenator is disclosed in several embodiments wherein the fibers either run at a transverse angle relative to the longitudinal axis of the oxygenator and/or are of a reduced length to optimize the gas transfer efficiency of the oxygenator. Various helical or spiral wraps of fibers are disclosed. One embodiment utilizes two sets of longitudinally extending fibers wherein the oxygen gas is moved in opposite directions from a central location of the oxygenator.