We have carried out systematic calculations for hydrogen-adsorption and -storage mechanism in carbon nanotubes at zero temperature. Hydrogen atoms first adsorb on the tube wall in an arch-type and zigzag-type up to a coverage of theta = 1.0 and are stored in the capillary as a form of H-2 molecule at higher coverages. Hydrogen atoms can be stored dominantly through the tube wall by breaking the C-C midbond, while preserving the wall stability of a nanotube after complete hydrogen insertion, rather than by the capillarity effect through the ends of nanotubes. In the hydrogen-extraction processes, H-2 molecule in the capillary of nanotubes first dissociates and adsorbs onto the inner wall and is further extracted to the outer wall by the flip-out mechanism. Our calculations describe suitably an electrochemical storage process of hydrogen, which is applicable for the secondary hydrogen battery.