  We consider the six-sphere S^6=G_2/SU(3) and its twistor space Z=G_2/U(2)
associated with the SU(3)-structure on S^6. It is shown that a Hermitian
Yang-Mills connection (instanton) on a smooth vector bundle over S^6 is
equivalent to a flat partial connection on a vector bundle over the twistor
space Z. The relation with Tian's tangent instantons on R^7 and their twistor
description are briefly discussed.
