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We consider the constant-roll condition in the model of the inflatonnonminimal coupling to the Gauss-Bonnet term. By assuming the firstGauss-Bonnet flow parameter $\delta_1$ is a constant, we discuss theconstant-roll inflation with constant $\epsilon_1$, constant $\epsilon_2$ andconstant $\eta_H$, respectively. Using the Bessel function approximation, weget the analytical expressions for the scalar and tensor power spectrum andderive the scalar spectral index $n_{\mathcal{R}}$ and the tensor to scalarratio $r$ to the first order of $\epsilon_1$. By using the Planck 2018observations constraint on $n_{\mathcal{R}}$ and $r$, we obtain some feasibleparameter space and show the result on the $n_{\mathcal{R}}-r$ region. Thescalar potential is also reconstructed in some spectral cases.

Gauss-Bonnet inflation with a constant rate of roll