In this study, we investigate the electronic properties of C-substituted YBa2Cu3O7 systems. In our study we use the full potential linearized augmented plane wave method within the density functional theory (DFT). We treat the exchange correlation energy using generalized gradient approach (GGA), Wu-Cohen GGA and local density approximation (LDA). The YBa2Cu3O7 has orthorhombic crystal system whose space group is Pmmm (47). The unit cell of YBa2Cu3O7 contains 13 atoms. We have found that the band gap energies of all crystal systems do not depend linearly on the carbon concentration. In addition for YBa2Cu3O4C3 crystal system, we show that the valence band and conduction band are overlapping. It means that, YBa2Cu3O4C3 has metallic properties. The calculated electronic charge densities reveal that carbon atoms are bonded to copper atoms with strong covalent bonds. These bonds are similar to the bonds between copper and oxygen atoms. This theoretical work motivates further future studies.