Electronic structure calculations based on density functional theory (DFT) within the generalized gradient approximation (GGA) and GGA+U for manganite cuprate compound LuCu 3 Mn 4 O 12 have been performed, using the full-potential linearized augmented plane wave method. The calculated results indicate that LuCu 3 Mn 4 O 12 is ferrimagnetic and half-metallic in both GGA and GGA+U calculations. The minority-spin band gap is 0.7eV within GGA, which is larger than that of LaCu 3 Mn 4 O 12 (0.3eV), indicating its better half-metallicity. Further, the minority-spin gap enlarges from 0.7 to 2.8eV with U taken into account, and simultaneously the Fermi level being shifted to the middle of the gap, making the half-metallic energy gap to be 1.21eV. These results demonstrate that electronic correlation effect enhances the stability of half-metallic property. These facts make this system interesting candidates for applications in spintronic devices.