We report a density functional calculation of the adsorption of molecular hydrogen on the external surface of coiled carbon nanotube (CCNT). Binding energies of single molecule have been studied as a function of three different orientations and at three different sites like hexagon, pentagon and heptagon. The binding energy values are larger than linear (5,5) armchair nanotube, which has approximately same diameter as that of coiled carbon nanotube. The curvature and topology of CCNT are responsible for this considerable enhancement. The system with full coverage is also studied. When the nanotube surface is fully covered with one molecule per graphitic hexagon, pentagon and heptagon gives the 6.8 wt% storage capacity. The binding energy per molecule decreases due to repulsive interactions between neighbor molecules. it gives good storage medium for hydrogen. Almost it meets the DOE target. (C) 2009 Professor T. Nejat Veziroglu. Published by Elsevier Ltd. All rights reserved.