Single crystals of the Ba-containing silicon clathrate superconductor Ba7.76Si46 were prepared using a high-pressure and high-temperature condition (3 GPa, 1300 degreesC). It crystallized in the cubic space group Pm-3n with a = 10.3141(7) Angstrom and Z = 1. There are two crystallographically different types of Ba sites, at the centers of Si clodecahederal (Ba@Si-20) and Si tetrakaidecahedral (Ba@Si-24) cages. On evacuation at 527 degreesC, a part of Ba atoms were removed from the Ba@Si-20 sites. The superconducting transition temperature (T-c) decreased from 9.0 to 6.0 K with the decrease of the Ba content from 7.76 to 6.63 Ba/Si-46. The Ba deficient sites and the deficiency were determined by the structural refinement in the single-crystal X-ray analyses.