We study the electronic and optical properties of the hydrogen boride sheet by using the many-body perturbation theory with the perturbative GW (G₀W₀) approximation. It was found that the hydrogen boride sheet shows a semimetallic electronic structure, supporting the previous theoretical study based on the semilocal density functional theory calculations. It was also found that the optical spectrum calculated based on the quasiparticle energies agrees well with the experiments. This work suggests that G₀W₀ approximation may be useful for predicting precise electronic and optical properties of the hydrogen boride sheet and its derivatives.