To analyze the oxygen solubility characteristics across the Ti-Zr-Nb-Ta quaternary composition space, we have varied each element’s composition in increments of 0.05, resulting in 1771 distinct compositions. For each composition, we construct a 6×6×6 supercell and iteratively place oxygen atom at each of all possible 1296 octahedral sites within the supercell. Using our trained ML model, we predict the oxygen solution energies for more than 2 million octahedral sites. The data file encompasses the average, standard deviation values, and the average spatial correlation coefficient up to 2NN for the predicted oxygen solution energies across the 1771 distinct compositions within the entire Ti-Zr-Nb-Ta composition space.