Hydroboron monoxide (HBO) is expected to occur in envelopes of the asymptotic giant branch (AGB), but a lack of spectroscopic data is hampering its possible detection. Using the state-of-the-art ab initio method, we present the first, comprehensive molecular line list for HBO which is suitable for temperatures up to T = 3000 K. This new line list covers the wavenumber range of 0-9000 cm-1 (wavelengths of λ ≥ 1.11 μm), and it contains almost 75 million transitions between 435 631 energy levels with rotational excitation up to J = 120. The new line list of HBO can facilitate its future molecular detection in the laboratory and interstellar space.