  We study the slow-roll single field inflation in the context of the
consistent $D\to4$ Einstein-Gauss-Bonnet gravity that was recently proposed in
\cite{Aoki:2020lig}. In addition to the standard attractor regime, we find a
new attractor regime which we call the Gauss-Bonnet attractor as the dominant
contribution comes from the Gauss-Bonnet term. Around this attractor solution,
we find power spectra and spectral tilts for the curvature perturbations and
gravitational waves (GWs) and also a model-independent consistency relation
among observable quantities. The Gauss-Bonnet term provides a nonlinear $k^4$
term to the GWs dispersion relation which has the same order as the standard
linear $k^2$ term at the time of horizon crossing around the Gauss-Bonnet
attractor. The Gauss-Bonnet attractor regime thus provides a new scenario for
the primordial GWs which can be tested by observations. Finally, we study
non-Gaussianity of GWs in this model and estimate the nonlinear parameters
$f^{s_1s_2s_3}_{\rm NL,\;sq}$ and $f^{s_1s_2s_3}_{\rm NL,\;eq}$ by fitting the
computed GWs bispectra with the local-type and equilateral-type templates
respectively at the squeezed limit and at the equilateral shape. For helicities
$(+++)$ and $( -- )$, $f^{s_1s_2s_3}_{\rm NL,\;sq}$ is larger while
$f^{s_1s_2s_3}_{\rm NL,\;eq}$ is larger for helicities $(++-)$ and $(--+)$.
