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