  We propose a novel {\it k}-Gauss-Bonnet inflationary model, in which a
kinetic term of scalar field is allowed to non-minimally couple to the
Gauss-Bonnet topological invariant in the absence of a potential of scalar
field. As a result, this model is shown to admit an isotropic power-law
inflation provided that the scalar field is phantom. Furthermore, stability
analysis based on the dynamical system method is performed to indicate that
this inflation solution is indeed stable and attractive. More interestingly, a
gradient instability in tensor perturbations is shown to disappear in this
model.
