  We study the main cosmological properties of the Generalized Chaplygin Gas
(GCG) dark energy model at the background and perturbation levels. By using the
latest cosmological data in both the background and perturbation levels, we
implement a joint likelihood analysis to constrain the cosmological parameters
of the model. Using the available expansion and growth rate data, we place
constraints on the free parameters of the GCG model based on the statistical
Markov chain Monte Carlo method. Then, the best-fit values of cosmological
parameters and those of confidence regions are found. We obtain the best-fit
value of the current expansion rate of the universe in the GCG model and show
that it is in good agreement with the $\Lambda$CDM model. Moreover, the growth
rate of matter perturbations is investigated in the context of a unified GCG
model. It is shown that in this model, the dark energy component, like the
$\Lambda$ sector in the $\Lambda$CDM model, can suppress the amplitude of
matter perturbations. We show that the growth rate of perturbations in GCG
parametrization is consistent with cluster-scale observations similar to the
case of the concordance $\Lambda$CDM model. Our results show that the tension
on $\sigma_{8}$ appeared in concordance model can be alleviated in GCG
cosmology.
