Density functional theory based calculations with Hubbard correction (DFT + U) were performed to investigate the effects of varying coverage and different adsorption sites on hydrogen (H) adsorption on zinc oxide (ZnO) (1010) surface. Results show that H adsorption on top of oxygen (O) at low coverage (0.25 monolayer, ML) shifts the conduction band below the Fermi level and narrows the band gap. These phenomena are attributed to the charge transfer between H and the surface zinc (Zn) and O atoms. On the other hand, the H adsorption on top of Zn at low coverage (0.25 ML) shows an overlapping of H, Zn, and O states while maintaining the semiconductor nature of the system. At high coverage (1.0 ML), a charge accumulation layer on the surface forms, and the mechanisms that govern the interactions of H atoms when adsorbed exclusively on top of Zn or top of O are found to be similar with the low coverage cases. Lastly, at full coverage (2.0 ML), the effect of H on top of Zn is more evident as the system retained its semiconducting property. The adsorption energy is enhanced due to the reinforced overlapping of the H, Zn, and O states and due to the possible attraction between the adsorbed H atoms. The properties and stability of full-coverage adsorption were explained based on the findings on high- and low- coverages adsorption. The findings of the study will aid in understanding the interaction of H with the ZnO surface toward the further development of ZnO’s optoelectronic applications.