  We will examine whether anisotropic hairs exist in a string-inspired
scalar-Gauss-Bonnet gravity model with the absence of potential of scalar field
during the inflationary phase. As a result, we are able to obtain the Bianchi
type I power-law solution to this model under the assumption that the scalar
field acts as the phantom field, whose kinetic is negative definite. However,
the obtained anisotropic hair of this model turns out to be large, which is
inconsistent with the observational data. We will therefore introduce a
nontrivial coupling between scalar and vector fields such as
$f^2(\phi)F_{\mu\nu}F^{\mu\nu}$ into the scalar-Gauss-Bonnet model with the
expectation that the anisotropic hair would be reduced to a small one.
Unfortunately, the magnitude of the obtained anisotropic hair is still large.
These results indicate that the scalar-Gauss-Bonnet gravity model with the
absence of potential of scalar field might not be suitable to generate small
anisotropic hairs during the inflationary phase.
