We report on a thermodynamic analysis of oxide vapor phase epitaxy (OVPE) of GaN. We first calculate equilibrium partial pressures of gases for the initial partial pressures of Ga2O, NH3, and H2 as well as the growth temperature. To estimate the growth rate of a GaN crystal, we then define the supersaturation amount determined by the equilibrium and initial partial pressures. In the calculation, the growth rate is significantly influenced by the initial partial pressures of Ga2O and NH3, while it is almost independent of the initial partial pressure of H2 and the growth temperature. Subsequently, we experimentally grow GaN crystals under same conditions as in the thermodynamic analysis. In the range of conditions in this work, the experimental growth rates are nearly consistent with the growth rates predicted by the thermodynamic analysis for all experimental parameters. Thus, the results showed that a high value of the supersaturation amount is advantageous for high-speed growth. Furthermore, we define the supersaturation ratio and investigate the correlation between this parameter and the surface coverage of the polycrystal. The surface coverage of the polycrystal is confirmed to roughly decrease as the value of the supersaturation ratio decreases. Thus, the results showed that a low value of the supersaturation ratio is advantageous for polycrystal-free growth. Finally, we use the thermodynamic analysis to explore the optimal conditions for high-speed and polycrystal-free growth. This revealed that the optimal OVPE growth conditions are both a high partial pressure of Ga2O and a low partial pressure of NH3.