The Ghost Dark Energy (GDE) model in varying Newton’s gravitational coupling (VG) theories is investigated. We first obtain the cosmological parameters of the model in modified FRW cosmology with varying G and then study the growth of matter perturbations in this formalism. Applying a Markov Chain Monte Carlo (MCMC) simulation and using the recent observational data, including Baryonic Acoustic Oscillation (BAO), the cluster X-ray Gas Mass Fraction (XGMF), Cosmic Microwave Background radiation (CMB), Growth Function for matter perturbation (GF), type Ia supernova (SNIa) and Hubble data, constraint results on GDE model parameters in VG theory are: Ω0m = 0.2751+0.0104+0.0208 −0.0104−0.0195, Ω0d = 0.7093+0.0123+0.0229 −0.0128−0.0245, β = −0.0156+0.0041+0.0082 −0.0042−0.0078 and H0 = 67.444+0.899+1.757 −0.873−1.829. The results for concordance ΛCDM model are: Ω0m = 0.2762+0.0097+0.0196 −0.0099−0.0188, Ω0d = 0.7238+0.0099+0.0188 −0.0097−0.0196, and H0 = 70.265+0.797+1.575 −0.797−1.515. We show that in this model the universe begins to accelerate at redshift zt 0.4 consistently in 1σ level with observations. It shows that the growth rate of this model is well fitted by observational growth data as the ΛCDM model.
