The structure of the HOI molecule was optimized at first, by employing the coupled cluster theory (CC) with single, double, and perturbative triple excitations (CCSD(T)), the iterative triple excitations (CC3) and its variants (CCSDT-3), and the B3LYP method from the density functional theory (DFT) in conjunct with the Dunning’s correlation consistent basis sets aug-cc-pVxZ/aug-cc-pVxZ-PP(x=T, Q, 5). Then, a series of discrete potential energy points were extracted nearby the equilibrium structure, which have been fitted to fourth-order polynominal expansion force field in normal coordinate. In addition, the anharmonic vibrational analysis were performed by the vibrational self-consistent field (VSCF), the vibrational configuration interaction (VCI) and the second-order vibrational perturbation theory (VPT2), the fundamental, overtone and combination (v1+v2+v3＝3), the rotational constants, the vibrational-rotational interaction constants, anharmonic constants, centrifugal distortion constants have been expected, the oscillator strength has been evaluated, and the effect of Deuterium substitution was investigated. The results show that: first, the present calculated values are in good agreement with available experimental results, spectroscopic constants from coupled cluster theory (CC) are more reliable than DFT, the deviation from DFT is obviously large, but it is quite consistent with the vibrational frequencies between CC and DFT; Second, it is not the larger basis set that causes the better coincidence between calculations and experiments, in general, the CC3 and CCSDT-3 results are more credible. Third, there is no resonance occurred in HOI or DOI.