X-ray absorption spectra (XAS) at the Cl and S K edge and Mo L edge have been calculated at the TDDFT level for a series of dioxomolybdenum complexes LMoO2X (L = hydrotris(3,5-dimethyl-l-pyrazolyl)borate, X = Cl, SCH2Ph, OPh), which play an important role in modeling the catalytic cycle of the sulfite oxidase enzyme. Also, the XAS spectra of model molecules of the Mo complexes have been simulated and interpreted in terms of the Mo 4d orbital splitting, in order to find possible correlations with the spectral pattern of the complexes. Comparison with the available experimental data allows us to assess the performances of the present computational scheme to describe the core excitations in large bioinorganic systems. The theoretical interpretation of the spectral features of both the metal and ligand core excitations in terms of the oscillator strength distribution provides important insight into the covalency of the metal-ligand bond.