The hydrogen dissolution behavior of the complex oxide SrCe0.95Yb0.05O3 was examined in the temperature range 500–1100 °C in an oxygen-water vapor atmosphere using a thermal desorption method. The partial pressures of water vapor pressure were controlled to be 870 and 3620 Pa, and the total pressure of the gas mixture of oxygen and water vapor was 105 Pa. Thermal desorption of H2 and H2O gases from the hydrogenated specimen was observed and inferred to be controlled by a surface reaction. The hydrogen solubility in SrCe0.95Yb0.05O3 was evaluated from the obtained thermal desorption spectra and found to range from 1 × 10−2 to 3 × 10−2 mol H (mol oxide)−1. The hydrogen solubility was found to decrease with increasing temperature and to increase with increasing water vapor pressure. The equilibrium between the atmosphere and the complex oxide was discussed in terms of a reaction involving oxygen vacancies and interstitial hydrogen defects.