We investigate the generalized Quantum Chromodynamics (QCD) ghost model of dark energy in the framework of Einstein gravity. First, we study the non-interacting generalized ghost dark energy in a flat Friedmann-Robertson-Walker (FRW) background. We obtain the equation of state parameter, w
D = p/ρ, the deceleration parameter, and the evolution equation of the generalized ghost dark energy. We find that, in this case, w
D cannot cross the phantom line (w
D > −1) and eventually the universe approaches a de-Sitter phase of expansion (w
D → −1). Then, we extend the study to the interacting ghost dark energy in both a flat and non-flat FRW universe. We find that the equation of state parameter of the interacting generalized ghost dark energy can cross the phantom line (w
D < −1) provided the parameters of the model are chosen suitably. Finally, we constrain the model parameters by using the Markov Chain Monte Carlo (MCMC) method and a combined dataset of SNIa, CMB, BAO and X-ray gas mass fraction.