Co2MnGa alloy was prepared by the conventional arc-melting method. The optical conductivity (OC) spectrum of the alloy was measured by a rotating-analyzer spectroscopic ellipsometer. The OC spectrum was also calculated based on the electronic structure by using the full-potential linearized-augmented-plane-wave method within the local-spin-density approximation to the density-functional theory. The calculated OC spectrum does not agree well with the experimental one. Since the Co2MnGa alloy could be a strongly-correlated material, the so-called 'LDA+U' method was applied with U = 5.4 eV. The calculated OC spectrum using the 'LDA+U' method agrees very well with the experimental one. The inclusion of the onsite Coulomb potential during the self-consistent calculation significantly modifies the minorityspin Co and Mn 3d bands, resulting in a contraction of the energy gaps between states which are strongly involved in interband absorption peaks. PACS. 78.66.Bz 78.20.Bh