Electrochemical oxygen redox reactions are the crucial elements for energy conversion and storage including fuel cells and metal air batteries. Despite tremendous research efforts, developing high-efficient, low-cost, and durable bifunctional oxygen catalysts remains a major challenge. We report a new class of hybrid material consisting of subnanometer thick amorphous cobalt hydroxide anchored on NCNT as a durable ORR/OER bifunctional catalyst. Although amorphous cobalt species-based catalysts are known as good OER catalysts, hybridizing with NCNT successfully enhanced ORR activity by promoting a 4e reduction pathway. Abundant charge carriers in amorphous cobalt hydroxide are found to trigger the superior OER activity with high current density and low Tafel slope as low as 36 mV/decade. A remarkably high OER turnover frequency (TOF) of 2.3 s(-1) at an overpotential of 300 mV was obtained, one of the highest values reported so far. Moreover, the catalytic activity was maintained over 120 h of cycling. The unique subnanometer scale morphology of amorphous hydroxide cobalt species along with intimate cobalt species-NCNT interaction minimizes the deactivation of catalyst during prolonged repeated cycles.