Abstract: The electronic structure and magnetic properties of the Ruddlesden-Popper (RP) layered perovskite Bi₈Ba₄Mn₈O₂₈ were investigated by using the projector augmented wave (PAW) pseudopotentials method based on the density functional theory. Due to the substitution of Ba in the A site, the rotation and tilt of the MnO₆ octahedra could be approved, and their impact on the electronic structure and magnetic properties were also discussed. The generalized gradient approximation calculation with the correction of the onsite Coulomb interaction (GGA+U) showed that the ground state of Bi₈Ba₄Mn₈O₂₈ is a ferromagnetic half-metal with a half-metallic gap of 3.07 eV and a total magnetic moment of 31μ_B. The magnetic moment of Bi₈Ba₄Mn₈O₂₈ is mainly contributed by the magnetic moment of Mn atoms, while the magnetic moments of Bi, Ba, and O atoms are relatively small. The half-metallicity is mainly due to the large exchange splitting between the spin-up and spin-down electrons of Mn 3d states. When the lattice constants vary in a wide range of -10% to 14%, the half-metallicity can be maintained and the total magnetic moment of the unit cell is always kept at 31μ_B.