Thermodynamic measurements on BaMoO₄, BaMoO₃ and BaMo₃O₁₀ are reported, that served as input for the development of a thermodynamic model of the Ba-Mo-O system using the CALPHAD methodology. The valence states of molybdenum in BaMoO₄ and BaMoO₃ were confirmed to be VI and IV, respectively, from X-ray Absorption Near Edge Structure Spectroscopy measurements at the Mo K-edge. The heat capacity at low temperatures of these compounds was obtained from thermal-relaxation calorimetry. Phase equilibrium data in the BaMoO₄-MoO₃ section were also measured, and the transition enthalpy associated with the peritectic decomposition of BaMo₃O₁₀ was determined using Differential Scanning Calorimetry. The developed thermodynamic model used the compound energy formalism for intermediate compounds, and an ionic two-sublattice model for the liquid phase. The optimized Gibbs energies were assessed with respect to the known thermodynamic and phase equilibrium data. A good agreement is generally obtained, but a number of ill-defined data were also identified.