We perform a global constraint on the Ricci dark energy model with both the flat case and the non-flat case, using the Markov Chain Monte Carlo (MCMC) method and the combined observational data from the cluster X-ray gas mass fraction, Supernovae of type Ia (397), baryon acoustic oscillations, current Cosmic Microwave Background, and the observational Hubble function. In the flat model, we obtain the best fit values of the parameters in 1 sigma, 2 sigma regions: Omega(m0) = 0.2927(-0.0388)(+0.0542), alpha = 0.3823(-0.0418-0.0541)(+0.0331+0.0415), Age/Gyr = 13.48(-0.16-0.21)(+0.13+0.17), H-0 = 69.09(-2.37-3.39)(+2.56+3.09). In the non-flat model, the best fit parameters are found in 1 sigma, 2 sigma regions: Omega(m0) = 0.3003(-0.0371-0.0423)(+0.0367+0.0429), alpha = 0.3845(-0.0474-0.0523)(+0.0386+0.0521), Omega(k) = 0.0240(-0.0130-0.0153)(+0.0109+0.0133), Lambda ge/Cyr = 12.54(-0.37-0.49)(+0.51+0.65), H-0 = 72.89(-3.05-3.72)(+3.31+3.388). Compared to the constraint results in the Lambda CDM model by using the same datasets, it is shown that the current combined datasets prefer the Lambda CDM model to the Ricci dark energy model.