We have systematically investigated the effect of hydrogen adsorption on a single BC₃ sheet as well as graphene using first-principles calculations. Specifically, a comparative study of the energetically favorable atomic configurations for both H-adsorbed BC₃ sheets and graphene at different hydrogen concentrations ranging from 1/32 to 4/32 ML and 1/8 to 1 ML was undertaken. The preferred hydrogen arrangement on the single BC₃ sheet and graphene was found to have the same property as that of the adsorbed H atoms on the neighboring C atoms on the opposite sides of the sheet. Moreover, at low coverage of H, the pattern of hydrogen adsorption on the BC₃ shows a proclivity toward formation on the same ring, contrasting their behavior on graphene where they tend to form the elongated zigzag chains instead. Lastly, both the hydrogenated BC₃ sheet and graphene exhibit alternation of semiconducting and metallic properties as the H concentration is increased. These results suggest the possibility of manipulating the bandgaps in a single BC₃ sheet and graphene by controlling the H concentrations on the BC₃ sheet and graphene.