The density functional theory is used to study the hydrogen storage abilities of alkali metal Li (Na, K), alkaline-earth metal Mg (Ca), and transition metal Ti (Ti, Sc, Y) decorated B-28, which is the possible smallest all-boron cage and contains one hexagonal hole and two octagonal holes. The most stable structure of B-28 explored by the calypso search is as same as that explored by Zhao et al. [Nanoscale 7(2015)15086]. It is calculated that the hollow sites outside of the cavities should be the most stable for all metals except for Ti. The average adsorption energy of H-2 molecules (E-ad) adsorbed by each Na (Ca, K, Mg, Sc, Y and Li) atom outside of the B28 cage are in the range from 0.2 to 0.6 eV, which is suitable for hydrogen storage under near-ambient conditions. However, the largest hydrogen gravimetric density (HGD) for the B28Sc3-12H(2) structure is smaller than the target of 5.5 wt% by the year 2017 specified by the US Department of Energy (DOE). Therefore, the metal Ti (Sc) decorated all-boron cage B-28 should not be good candidates for hydrogen storage. The calculated desorption temperature and the molecular dynamic simulation indicate that the B28M3-nH(2) (M = Na, Li, Ca, K, Mg, Y) structures are easy to desorb the H-2 molecules at the room temperature (T = 300 k). Furthermore, the B-28 cages bridged by the sp(2)-terminated B-5 chain can hold Na (Li, Ca, K, Mg, Y) atoms to capture hydrogen molecules with moderate Bad and HGD. These findings suggest a new route to design hydrogen storage materials under the near-ambient conditions. (C) 2017 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.