Heavily $p^{ ＋}$-typed ($10^{20}$ $cm^{-3}$ ) GaAs epilayers have been grown on high-index GaAs substrates with various crystallographic orientations from (100) to (111)A by a low-pressure metalorganic chemical vapor deposition. Carbon (C) tetrabromide (CBr$_4$) was used as a C source. At moderate growth temperatures and high V/III ratios, the hole concentration of C-doped GaAs epilayers shows the crystallographic orientation dependence. The bonding strength of As sites on a growing surface plays an important role in the C incorporation into the high-index GaAs substrates.