Trivalent rare-earth holmium ion (Ho³⁺) doped yttrium oxide (Y₂O₃) has attracted great research interest owing to its unique optoelectronic properties and excellent performances in many new-type laser devices. But the crystal structures of the Ho³⁺-doped Y₂O₃ system (Y₂O₃ : Ho) are still unclear. Here, we have carried out a first-principle study on the structural evolution of the trivalent Ho³⁺ doped Y₂O₃ by using the CALYPSO structure search method. The results indicate that the lowest-energy structure of Ho³⁺-doped Y₂O₃ possesses a standardized monoclinic P2 phase. It is found that the doped Ho³⁺ ion are likely to occupy the sites of Y³⁺ in the host crystal lattice, forming the [HoO₆]⁹⁻ local structure with C₂ site symmetry. Electronic structure calculations reveal that the band gap value of Ho³⁺-doped Y₂O₃ is approximately 4.27 eV, suggesting the insulating character of Y₂O₃ : Ho system. These findings could provide fundamental insights to understand the atomic interactions in crystals as well as the information of electronic properties for other rare-earth-doped materials.