  In this paper we extend the form of interaction term into the non-linear
regime in the ghost dark energy model. A general form of non-linear interaction
term is presented and cosmic dynamic equations are obtained. Next, the model is
detailed for two special choice of the non-linear interaction term. According
to this the universe transits at suitable time ($z\sim 0.8$) from deceleration
to acceleration phase which alleviate the coincidence problem. Squared sound
speed analysis revealed that for one class of non-linear interaction term
$v_s^2$ can gets positive. This point is an impact of the non-linear
interaction term and we never find such behavior in non interacting and
linearly interacting ghost dark energy models. Also statefinder parameters are
introduced for this model and we found that for one class the model meets the
$\Lambda CDM$ while in the second choice although the model approaches the
$\Lambda CDM$ but never touch that.
