  Recently, an interesting inflationary scenario, named Gauss-Bonnet inflation,
is proposed by Kanti et al.~\cite{Kanti:2015pda,Kanti:2015dra}. In the model,
there is no inflaton potential but the inflaton couples to the Guass-Bonnet
term. In the case of quadratic coupling, they find inflation occurs with
graceful exit. The scenario is attractive because of the natural set-up.
However, we show there exists the gradient instability in the tensor
perturbations in this inflationary model. We further prove the no-go theorem
for the Gauss-Bonnet inflation without an inflaton potential.
