Catalytic doping is important for enhancing the hydrogen storage performance of metal hydrides, but it is challenging to develop a single catalyst to enhance both hydrogen desorption and absorption to a certain degree. Herein, a bidirectional Co/Pd catalyst, homogeneously loaded on bamboo-shaped carbon nanotubes (Co/Pd@B-CNTs), showed superior catalytic effects, improving both the hydrogen desorption and absorption properties of MgH2 at relatively low temperatures. The MgH2–Co/Pd@B-CNTs composite starts to release hydrogen at 198.9 °C, which is 132.4 °C lower than as-milled MgH2. The hydrogen desorption activation energy for MgH2 is reduced from 178.00 to 76.66 kJ mol−1 by the catalytic effects of Co/Pd@B-CNTs. The MgH2–Co/Pd@B-CNTs composite shows dramatically improved absorption kinetics; it rapidly uptakes 6.68 wt% H2 within 10 s at 250 °C, and quickly absorbs 1.91 wt% H2 within 100 s, even at a temperature as low as 50 °C. More importantly, a special mechanism for the “bidirectional catalyst” Co/Pd is proposed for the first time and discussed in detail. During the hydrogenation process, elemental Pd plays a dominant role in accelerating the preferential diffusion of hydrogen atoms at the Pd/Mg interface, while during dehydrogenation, phase transformation between Mg2Co and Mg2CoH5 as well as a Mg–Pd alloy becomes the crucial factor, facilitating the release of hydrogen atoms by decreasing the diffusion barrier. Moreover, novel structures of bamboo-shaped carbon nanotubes with a large diameter (>100 nm) and high specific surface area (146.8 m2 g−1) allow the homogenous dispersion of Co/Pd NPs and enhance the direct contact with MgH2 particles.