In this paper, we study the $R^2$ corrections to the spectral functions of heavy mesons in Gauss-Bonnet gravity. We discuss the effect of Gauss-Bonnet parameter $\lambda_{GB}$ on the 1S states and 2S states of charmonium and bottomonium. It is found that $\lambda_{GB}$ reduces the height and increases the width of the 1S states peak. The 2S states of charmonium and bottomonium dissociate gradually as increasing $\lambda_{GB}$. It is obvious that $\lambda_{GB}$ enhances the dissociation of charmonium and bottomonium.
Comment: 13 pages, 4 figures