A new 8-layer shifted hexagonal perovskite Ba8MnNb6O24 has been synthesized in air, featuring unusual long-range B-cation ordering with single octahedral high-spin d(5) Mn2+ layers separated by similar to 1.9 nm within the corner-sharing octahedral d(0) Nb5+ host, analogous to Ba-8(Zn/Co)Nb6O24. The large size and charge differences between high-spin Mn2+ and Nb5+, as well as the out-of-center distortion of NbO6 octahedra associated with the bonding covalence and second-order Jahn-Teller effect of Nb5+, drive long-range cationic ordering, thus stabilizing Ba8MnNb6O24. The Ba8MnNb6O24 pellet exhibits a high dielectric permittivity, epsilon(r) similar to 38, and a large temperature coefficient of resonant frequency, tau(f) similar to 20 ppm/K, but a dielectric loss (Q(f) similar to 987 GHz) and conductivity (similar to 10(-8)-10(-3) S/cm within 473-1173 K) much higher than those of Ba8ZnNb6O24. Electronic structures from density functional theory calculations reveal that Ba8MnNb6O24 is a Mott insulator in contrast with the charge-transfer insulator nature of Ba8ZnNb6O24, and they confirm that the off-center distortion of Nb5+ contributes to stabilization of the 8-layer ordered shifted structure. The contrast between conductivity and dielectric loss of Ba8MnNb6O24 and Ba8ZnNb6O24 is understood based on the electronic structure that depends on high-spin d(5) Mn2+ and d(10) Zn2+ cations. The hopping of 3d valence electrons in high-spin Mn2+ to Nb5+ 4d conduction bands over a small gap (similar to 2.0 eV) makes Ba8MnNb6O24 more conductive than Ba8ZnNb6O24, where the electrons are conducted via the hopping of a lattice O 2p valence electron to the Nb5+ 4d conduction bands over a larger gap (similar to 3.9 eV). The high microwave dielectric loss of BMN may be mainly ascribed to the half-filled Mn 3d orbits, which is understood based on the softened infrared modes that increase the lattice vibration anharmonicity as well as the resonant spin excitation of unpaired d electrons.