We have calculated theoretical UV-vis absorption spectra for tetrahedral MoS42- and [(NC)CuS2MoS2](2-) anions by the use of DV-X alpha cluster method. The calculated spectra for both anions are in good agreement with the experiments. The results show that the first and the second band in the spectra for both anions are principally caused by the electronic transitions within the MoS4 core, relating to the HOMO 1t(1) and LUMOs 2e and 3t(2). The third band is sensitively affected by the structure of MoS4 core and its environment, In the case of simple MoS42- anion, the third band not only shifts by the Mo-S bond length but also is expected to change the structure by its environment The third band of [(NC)CuS2MoS2](2-) is changed by the interaction among Cu 3d, Mo 4d, and S 3p orbitals, We have also tried to clarify the real structure of MoS42- anion in the actual solution, by calculating various clusters with different Mo-S distances, and have found the cluster with the bond length of 2.22 Angstrom provided the best fit to the experimental spectrum.