We investigate the correspondence relation between f (R) gravity and an interacting holographic dark energy (HDE). By obtaining the conditions needed for some observational evidence such as positive acceleration expansion of the Universe, crossing the phantom divide line and validity of the thermodynamics second law in an interacting HDE model and corresponding it with the f (R) model of gravity, we find a viable f (R) model that can explain the present Universe. We also obtain the explicit evolutionary forms of the corresponding scalar field, potential and scale factor of the Universe.
