Using density functional theory, we have studied surface structural and electronic properties of sulfur adsorption on As-terminated and In-terminated InAs(001) surfaces with the coverage (Θ) of 0.5ML and 1ML. Based on adsorption energy calculations, we found that at Θ=0.5ML, S adatoms preferred to replace the As atoms at As-terminated InAs(001)(2×1) surface. For 1ML S adsorption on InAs(001)(2×1) surface, the most stable adsorption geometry is S-S dimers covered on the In-terminated surface. This result is different from that for 1ML S adsorption on GaP(001) and InP(001) surfaces, and it is consistent with the experimental results. The electronic band structure analysis showed that the surface state density around the Fermi level was considerably diminished for 0.5ML S adsorption on As-terminated InAs(001)(2×1) surface at substitution site. The surface state density of S-S dimer adsorption on In-terminated (2×1) surface was strengthened due to one excess valence electron on the surface.