To accurately predict the full-range mechanical behavior of prestressed concrete composite box girders with corrugated steel webs (PCCBGCSWs) subjected to pure torsion, a theoretical model called “the improved softened membrane model for torsion (ISMMT)” was proposed based on the softened membrane theory. First, the equilibrium equations, compatibility equations, constitutive laws of materials and general solution algorithm of the ISMMT were briefly introduced. On this basis, a simplified solution algorithm was additionally presented for the stage when both steel bars, the prestressing steel and the corrugated steel webs (CSWs) are in the elastic state, which contains only one iteration loop. To validate the feasibility and accuracy of the ISMMT, a PCCBGCSW specimen was tested under pure torsion. The results, including the overall torque-twist curve, shear strains in the CSWs and concrete flanges, and strains in the prestressing steels and steel bars, were obtained from the test. Then, the experimental results were compared with the theoretical results calculated by the ISMMT. The comparison of solving efficiency between the general computer program and the simplified one was also conducted. Results show that the ISMMT not only can provide accurate prediction for the full-range torque-twist curve of PCCBGCSWs under pure torsion, but also can make precise predictions for the entire stress evolution in components of the PCCBGCSWs during loading, including the concrete flanges, CSWs, prestressing steels, and steel bars. When using the ISMMT to predict the full-range behavior of the PCCBGCSW specimen under pure torsion in this study, the number of iterations could be as high as 7.9 × 106 if the general computer program was used. However, if the simplified computer program was employed, the number of iterations could be significantly reduced (5 times at least and 193 times at most), which is a great improvement in solving efficiency in comparison with the general computer program. Therefore, the ISMMT provides an effective way to analyse the full torsional behaviour of PCCBGCSWs under pure torsion.