The ordinary and entropy-corrected versions of the holographic dark energy models in the spatially flat Friedmann–Robertson–Walker universe are considered. Then the F(G) modified gravity models as a candidates of dark energy are reconstructed according to the ordinary and entropy-corrected versions of the holographic dark energy models. The EoS parameters corresponding to the F(G) gravity models are obtained. The validity phantom or quintessence models in this framework of the modified gravity are investigated.
