To screen and use ionic liquids (LLs) as environmental-friendly extractive solvents in removing aromatic sulfur compounds (S-compounds) from fuel oils, the knowledge of their capacity for S-compounds (or solubility of S-compounds in ILs) is very important. In this work, the capacities of 1860 potential ILs (30 anions, 62 cations) for two representative S-compounds of thiophene (TS) and dibenzothiophene (DBT) are calculated using conductor-like screening model for real solvents (COSMO-RS). The influences of cation family, cation alkyl chain length, cation symmetry, anion nature, anion alkyl chain length, and functional group on the capacity are extensively discussed and are understood from microlevel view with a-profile, a-moments, and COSMO-RS energies. It is observed that the capacity is very dependent on cation and anion structure characteristics and is in a very wide range (e.g., 10(-3)similar to 10(1) for TS, 10(-3)similar to 10(2) for DBT); the van der Waals (vdW) and hydrogen-bonding (HB) energies have significant effects on the capacity. Increasing the nonpolarity and vdW energies of cation or alkyl chain on anion, or the polarity and HB energies of anion, can favor the capacity. This work is valuable to rationally select or design the ILs for desulfurization of fuel oils.