ABSTRACT Zirconium monoxide (ZrO) absorption lines define rare S-type stars and are currently being sought on exoplanets. Successful detection is dependent on an accurate and comprehensive line list, with existing data not ideal for many applications. Specifically, the Plez et al. line list is near-complete but has insufficient accuracy for high-resolution cross-correlation, while the Sorensen & Bernath data have high accuracy but only consider a small number of spectral bands. This article presents a novel spectroscopic model, variational line list, and trihybrid line list for the main 90Zr16O isotopologue, as well as isotopologue-extrapolated hybrid line lists for the 91Zr16O, 92Zr16O, 93Zr16O, 94Zr16O, and 96Zr16O isotopologues. These were constructed using Duo based on icMRCI-SD/CASSCF ab initio electronic data calculated using molpro, experimental energies obtained from a previous MARVEL data compilation, and perturbative energies from Sorensen & Bernath. The new 90Zr16O ExoMol-style trihybrid line list, ZorrO, comprises 227 118 energies (13 075 experimental) and 47 662 773 transitions up to 30 000 cm −1 (333 nm) between 10 low-lying electronic states (X 1Σ+, a 3Δ, A 1Δ, b 3Π, B 1Π, C 1Σ+, d 3Φ, e 3Π, f 3Δ, and F 1Δ). The inclusion of experimental energy levels in ZorrO means ZrO will be much easier to detect using high-resolution ground-based telescopes in the 12 500–17 500 cm−1 (571–800 nm) spectral region. The inclusion of variational energy levels means that the ZorrO line list has very high completeness and can accurately model molecular absorption cross-sections even at high temperatures. The ZorrO data will hopefully facilitate the first detection of ZrO in the atmosphere of a hot Jupiter exoplanet, or alternatively more conclusively exclude its presence.