  We investigate the structure formation in the effective field theory of the
holographic dark energy. The equation of motion for the energy contrast
$\delta_m$ of the cold dark matter is the same as the one in the general
relativity up to the leading order in the small scale limit $k\gg aH$, provided
the equation of state is Quintessence-like. Our effective field theory breaks
down while the equation of state becomes phantom-like. We propose a solution to
this problem by eliminating the scalar graviton.
