Facilitated oxygen transport is an effective strategy for the oxygen transport that may enhance the oxygen permeance and its selectivity, which may provide oxygen rich permeate that can be used in medical applications as in the present COVID-19 pandemic situation for providing the sufficient oxygen to the patients. This study presents the bio-inspired oxygen transport by covalently bonded Cobalt Phthalocyanine complex anchored on multi walled carbon nanotube (MWCNT) via axial ligand, incorporated in PDMS hollow fiber membranes with 0.05, 0.1, 0.5 and 1.0 wt % loadings. Successful functionalization of MWCNT was confirmed by Raman spectroscopy and X-ray photoelectron spectroscopy. The membranes were thoroughly characterized by using FE-SEM with elemental mapping, ATR-IR, DSC and TGA analysis. It demonstrated facilitated oxygen transport through the covalently immobilized Cobalt complex of the membrane with high oxygen permeance of 49 GPU as well as exceptional oxygen selectivity of 17 at 0.5 wt % Cobalt Phthalocyanine@ MWCNT loading. These values are highest among the known Cobalt complex based hollow fiber composite membranes in the literature suggesting its best utility in selective oxygen concentration for practical applications.