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 B28, which is the possible smallest all-boron cage and contains one hexagonal hole and two octagonal holes. The most stable structure of B28 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 H2 molecules (Ead) 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 B28Sc3-12H2 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 B28 should not be good candidates for hydrogen storage. The calculated desorption temperature and the molecular dynamic simulation indicate that the B28M3-nH2 (M = Na, Li, Ca, K, Mg, Y) structures are easy to desorb the H2 molecules at the room temperature (T = 300 k). Furthermore, the B28 cages bridged by the sp2-terminated B5 chain can hold Na (Li, Ca, K, Mg, Y) atoms to capture hydrogen molecules with moderate Ead and HGD. These findings suggest a new route to design hydrogen storage materials under the near-ambient conditions.