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A new dark energy model called "ghost dark energy" was recently suggested to explain the observed accelerating expansion of the universe. This model originates from the Veneziano ghost of QCD. The dark energy density is proportional to Hubble parameter, $\rho_D=\alpha H$, where $\alpha$ is a constant of order $\Lambda_{\rm QCD}^3$ and $\Lambda_{\rm QCD}\sim 100 MeV$ is QCD mass scale. In this paper, we extend the ghost dark energy model to the universe with spatial curvature in the presence of interaction between dark matter and dark energy. We study cosmological implications of this model in detail. In the absence of interaction the equation of state parameter of ghost dark energy is always $w_D > -1 $ and mimics a cosmological constant in the late time, while it is possible to have $w_D < -1 $ provided the interaction is taken into account. When $k = 0$, all previous results of ghost dark energy in flat universe are recovered. To check the observational consistency, we use Supernova type Ia (SNIa) Gold sample, shift parameter of Cosmic Microwave Background radiation (CMB) and the Baryonic Acoustic Oscillation peak from Sloan Digital Sky Survey (SDSS). The best fit values of free parameter at $1\sigma$ confidence interval are: $\Omega_m^0= 0.35^{+0.02}_{-0.03}$, $\Omega_D^0=0.75_{-0.04}^{+0.01}$ and $b^2=0.08^{+0.03}_{-0.03}$. Consequently the total energy density of universe at present time in this model at 68% level equates to $\Omega_{\rm tot}^0=1.10^{+0.02}_{-0.05}$
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