  We study inflationary models with a Gauss-Bonnet term to reconstruct the
scalar field potentials and the Gauss-Bonnet coupling functions from the
observable quantities. Using the observationally favored relations for both
$n_s$ and $r$, we derive the expressions for both the scalar field potentials
and the coupling functions. The implication of the blue-tilted spectrum,
$n_t>0$, of the primordial tensor fluctuations is discussed for the
reconstructed configurations of the scalar field potential and the Gauss-Bonnet
coupling.
