In accordance with safety requirements for the near-surface disposal of low and medium-level radioactive solid waste, accurate identification and measurement of radionuclide types and activities within steel boxes containing such waste are necessary. Conventional sampling techniques are impractical due to nonuniform internal filling and radioactive distribution in the steel boxes used for storage. Nondestructive measurement analysis techniques offer significant advantages by providing comprehensive measurements without causing damage to the steel boxes or generating secondary waste. Therefore, nondestructive techniques are widely applicable and superior to chemical analysis methods. This study presents an algorithm for analyzing γ-ray spectrum measurements of radioactive solid waste steel boxes by combining the traditional computed tomography (CT) principle with a discrete treatment approach. The progressive split voxel measurement method is utilized to discretely handle the radioactive solid waste steel boxes during the measurement and calculation process while considering the impact of voxel interactions on detection efficiency. A detection efficiency calibration model is established using Monte Carlo (MC) simulation in conjunction with the algebraic reconstruction technique (ART). Additionally, an inversion correction of the efficiency for the physically coincident portion of the detected voxel volume is performed during the measurement process. The proposed algorithm is initially applied to the analysis platform of steel boxes that store FA-IV-type radioactive solid waste. The algorithm's performance is further investigated and validated using standard radioactive sources with known activity levels. The results indicate that the relative deviation between the reconstruction results and the nominal values of radioactive activities in the steel boxes is less than 30%. These findings align with the expected results and satisfy the measurement analysis and warehousing processing requirements for waste generated from the decommissioning of China's 101 nuclear reactor. The proposed algorithm holds great potential for widespread application in related detection work.