  The interacting dark energy model could propose a effective way to avoid the
coincidence problem. In this paper, dark energy is taken as a fluid with a
constant equation of state parameter $w_x$. In a general gauge, we could obtain
two sets of different perturbation equations when the momentum transfer
potential is vanished in the rest frame of dark matter or dark energy. There
are many kinds of interacting forms from the phenomenological considerations,
here, we choose $Q=3H\xi_x\rho_x$ which owns the stable perturbations in most
cases. Then, according to the Markov Chain Monte Carlo method, we constrain the
model by currently available cosmic observations which include cosmic microwave
background radiation, baryon acoustic oscillation, type Ia supernovae, and
$f\sigma_8(z)$ data points from redshift-space distortion. Jointing the
geometry tests with the large scale structure information, the results show a
tighter constraint on the interacting model than the case without
$f\sigma_8(z)$ data. We find the interaction rate in 3$\sigma$ regions:
$\xi_x=0.00372_{-0.00372- 0.00372-0.00372}^{+0.000768+0.00655+0.0102}$. It
means that the recently cosmic observations favor a small interaction rate
between the dark sectors, at the same time, the measurement of redshift-space
distortion could rule out a large interaction rate in the 1$\sigma$ region.
