A new caged Cu-rich antimonide, BaCu7.31(3)Sb5, was obtained from a direct combination of the elements in a graphite crucible under a high vacuum by a solid state reaction, and the structure was determined by the single-crystal X-ray diffraction method to be hexagonal P6(3)/mmc (No.194), with a=7.0154(4) angstrom, c=12.5423(14) angstrom, V=534.58(7) angstrom(3), and Z= 2. BaCu7.31(3)Sb5 is the first antimonide member of the BaNi9P5-type barium copper pnictides with a Cu2 site occupancy of 43.7(9)%, and the structure building unit is a 30-vertex Cu18Sb12 cage centered by a Ba atom. The Cu18Sb12 cages form chains along the c axis by sharing the opposite hexagonal (Cu-2)(3)(Sb-2)(3) faces. Such a cage chain shares (Cu1)(2)(Sb1)(2) rhomboidal faces with six neighboring chains along the [100], [010], and [110] directions to generate a 3D condensed metallic network. The electronic structure calculations by CASTEP indicate the metallic nature, which matches well with the metallic electrical conductivity, small Seebeck coefficient, and Pauli paramagnetism. The calculated formation energies indicate that BaCu7.5Sb5 Ba2Cu15Sb10 with the Cu2 site ha ff occupied is the energetically favorable stoichiometry compared with Ba2Cu12Sb10 (empty Cu2 site) and Ba2Cu18Sb10 (fully occupied Cu2 site).