By using a Markov Chain Monte Carlo simulation, we investigate cosmological constraints on the ghost dark energy (GDE) model in the framework of the Brans–Dicke (BD) theory. A combination of the latest observational data of the cosmic microwave background radiation data from seven-year WMAP, the baryon acoustic oscillation data form the SDSS, the supernovae type Ia data from the Union2 and the X-ray gas mass fraction data from the Chandra X-ray observations of the largest relaxed galaxy clusters are used to perform constraints on GDE in the BD cosmology. In this paper, we consider both flat and non-flat universes together with interaction between dark matter and dark energy. The main cosmological parameters are obtained as: Ωbh2=0.0223+0.0016−0.0013 , Ωch2=0.1149+0.0088−0.0104 and Ωk=0.0005+0.0025−0.0073 . In addition, the Brans–Dicke parameter ω is estimated as 1/ω≃0.002 .