Developing stable metal-free materials with a highly efficient hydrogen evolution reaction (HER) has received intense research interest due to its renewable and environmentally friendly properties. In this work, we systematically investigated the HER catalytic activity of a new h-B2O monolayer based on first-principles calculations. The results show the B site in the h-B2O structure is energetically favorable for hydrogen with the calculated Gibbs free energy (ΔGH*) of −0.07 eV, which is comparable to that of the Pt catalyst (ΔGH* = −0.09 eV). Moreover, the catalytic activity of the h-B2O monolayer is quite robust with increasing hydrogen coverages (from 1/9 to 9/9). Interestingly, the HER activity of the h-B2O monolayer is sensitive to the strains-driven. For example, applied tensile strains (0–2%) could weaken the bonding between hydrogen and the substrate, resulting in ΔGH* even close to 0 eV. However, the opposite trend is found for applied compressive strain. After analyzing the density of states (DOS), we found the h-B2O monolayer with absorbed hydrogen retains the metallic property, still exhibiting excellent electrical conductivity. These results reveal that the metal-free h-B2O monolayer is a promising candidate for HER applications.