We investigate the crystal growth of BiSb thin films on various GaAs substrates with different crystal orientation and surface termination. We found the non-trivial growth mode of BiSb which depends on the crystal orientation/ surface termination of GaAs. While BiSb(0 0 1) can be grown epitaxially on GaAs(111) A, only textured BiSb(0 12) can be grown on GaAs(111) B even with the help of an ultrathin Bi buffer layer, indicating the critical role of surface termination of the GaAs(111) substrates. Meanwhile, only textured BiSb(0 0 1) thin films grow on GaAs(0 0 1) instead of BiSb(0 12), indicating that symmetry matching plays a little role on the growth of BiSb on GaAs(0 0 1).