We present the results of investigations on the muon sitesin YBa2Cu3O6(YBCO6) by using the density functional theory (DFT) calculation technique in order to achieve a deeper understanding of its magnetic properties. We included the Hubbard parameter, U, among electrons in our DFT calculations in order to simulate realistic electronic and magnetic state in YBCO6. We found that the U value does not affect the muon sites in YBCO6but the related internal field has strong dependence on U value. In this study, we tried to optimize the value of Ucomparing with the experimental result.