  We investigate the instability of the ghost dark energy model against
perturbations in different cases. To this goal we use the squared sound speed
$v_s^2$ whose sign determines the stability of the model. When $v_s^2<0$ the
model is unstable against perturbation. At first we discuss the noninteracting
ghost dark energy model in a flat FRW universe and find out that such a model
is unstable due to the negativity of the $v_s^2$ in all epoches. The
interacting ghost dark energy model in both flat and non-flat universe are
studied in the next parts and in both cases we find that the squared sound
speed of ghost dark energy is always negative. This implies that the perfect
fluid for ghost dark energy is classically unstable against perturbations. In
both flat and non flat cases we find that the instability of the model
increases with increasing the value of the interacting coupling parameter.
