The polymer-alloy geocell sheets (PAGS) represent a novel geocell material developed to replace conventional geocell materials. Accelerated creep testing, a convenient and precise performance evaluation method, presents a viable alternative to traditional creep testing for obtaining long-term creep strains. Nonetheless, there is a lack of prediction and in-depth exploration of accelerated creep testing. This paper aims to assess the efficacy of using the non-linear three-component (NLTC) model to simulate the accelerated creep behavior of PAGS. The predictive accuracy of the NLTC model has undergone evaluation through a comparison between stepped isothermal method (SIM) accelerated creep experimental tests and numerical simulations. Subsequently, the validated NLTC model was employed to simulate the time-temperature superposition method (TTSM), time-stress superposition method (TSSM), and stepped isostress method (SSM) accelerated creep tests, thereby verifying its effectiveness in predicting all accelerated creep tests. The results indicate that the NLTC model can effectively simulate creep deformation induced by temperature increases, particularly the temperatures below 41 °C. Although some errors are observed at elevated temperatures, it is within the acceptable range of 17.4%. Numerical simulation results of TTSM, TSSM, and SSM tests also suggest the model's proficiency in simulating the accelerated creep behavior by temperature and creep load increasing.