Ba8CuTa6O24-delta ceramics possess exceptionally high microwave dielectric loss among the eight-layer twinned hexagonal perovskite Ba8MTa6O24 (M=Zn, Co, Ni, Mg, Cu) analogs. Impedance spectroscopy measurement demonstrates that the eight-layer Ba8CuTa6O24-delta ceramics show the electrical heterogeneous microstructure, consisting of leaky insulating grains and more resistive grain boundary regions. This induced internal barrier layer capacitance (IBLC) effects on Ba8CuTa6O24-delta ceramics. The heterogeneous electrical microstructure is associated with partial reduction of Cu2+ to Cu+ and oxygen loss during the sintering procedure and limited reoxidization along grain boundary regions on cooling. The existence of Cu+ in Ba8CuTa6O24-delta ceramic is confirmed by X-ray photoelectron spectroscopy measurement. The leaky insulating bulk property for the Ba8CuTa6O24-delta ceramics is compared with the highly insulating bulk behavior of other low dielectric loss analogs, which indicates that the significant defects of Cu+ and oxygen vacancies are responsible for the high microwave dielectric loss of the Ba8CuTa6O24-delta ceramics.