  In this paper we investigate ghost dark energy model in the presence of
non-linear interaction between dark energy and dark matter. We also extend the
analysis to the so called generalized ghost dark energy (GGDE) which
$\rho_D=\alpha H+\beta H^2$. The model contains three free parameters as
$\Omega_D, \zeta(=\frac{8\pi G \beta}{3})$ and $b^2$ (the coupling coefficient
of interactions). We propose three kinds of non-linear interaction terms and
discuss the behavior of equation of state, deceleration and dark energy density
parameters of the model. We also find the squared sound speed and search for
signs of stability of the model. To compare the interacting GGDE model with
observational data sets, we use more recent observational outcomes, namely SNIa
from JLA catalog, Hubble parameter, baryonic acoustic oscillation and the most
relevant CMB parameters including, the position of acoustic peaks, shift
parameters and redshift to recombination. For GGDE with the first non-linear
interaction, the joint analysis indicates that $\Omega_D=0.7192\pm0.0062$,
$b^2=0.146^{+0.030}_{-0.026}$ and $\zeta=0.104\pm0.047$ at 1 optimal variance
error. For the second interaction, the best fit values at $1\sigma$ confidence
are $\Omega_D=0.72091\pm0.0065$, $b^2=0.0395\pm0.0080$ and $\zeta\le0.0173$.
According to combination of all observational data sets considered in this
paper the best fit values for third non-linearly interacting model are
$\Omega_D=0.7287\pm0.0062$, $b^2=0.0109\pm0.0023$ and $\zeta\le0.00764$ at
$1\sigma$ confidence interval. Finally we found that the presence of
interaction is compatible in mentioned models via current observational data
sets.
