We report first-principles calculations to determine the structural and electronic properties of Er0.5Lu0.5B2 and LuB2 compounds, by using Density Functional Theory (DFT) and Full Potential Linearized Augmented Plane-Waves (FP-LAPW) method. For the description of the electron-electron interaction was used the Local Density Approximation (LDA), Generalized Gradient Approximation of Perdew-Burke-Ernzerhof (GGA-PBE) and PBE0 hybrid functional. From the density of states (DOS), it is found that the addition of a fraction of the exact Hartree- Fock exchange energy in PBE approximation, evidence the localization of the 4f-Er and 4f-Lu orbitals, which favours the polarization of the electronic spins of these orbitals in LuB2 and Er0.5Lu0.5B2 compounds. The PBE0 scheme is justified because it describes of more appropriate manner the electronic and magnetic properties of strongly correlated systems than the LDA and PBE approaches.