Acid-washed solutions containing various ions, including uranium, are produced by washing uranium-bearing soil or minerals with H2SO4. Conventional extraction processes are complex, as they involve multiple steps and generate significant amounts of radioactive organic waste, posing environmental risks. Therefore, it is necessary to develop a simplified process that can selectively extract uranium while minimizing radioactive waste production. In this study, thermodynamic equilibrium calculations were performed to investigate the selective extraction of uranium through its reaction with H2O2. A basic additive was introduced to facilitate this reaction. The calculation results indicated that uranium in acid-leached solutions could be selectively extracted through a single-step precipitation process, which was experimentally validated. These findings can be utilized to design an efficient process for obtaining high-purity uranium from uranium-bearing soil or minerals.