To address the problem that the variable time delay seriously affects the stability and accuracy of the real-time hybrid simulation（RTHS），a robust time-delay compensation method was studied. A feedback controller based on H∞ robust control method of mixed sensitivity was designed to stabilize the dynamics of the testing system，while the polynomial extrapolation method was employed to compensate for the time-delay. The proposed method was applied to a linear Benchmark problem. To further investigate the performance of the proposed method，virtual RTHSs were carried out with linear and nonlinear physical substructure（PS） employing linear and nonlinear models of the loading system. The results showed the measured displacements were almost identical to the desired displacements. Compared with the existing method，RTHS with the robust time-delay compensation method had a smaller error. For nonlinear PS，the root-mean-square error（RMSE） and peak error（PE） were both between 0.6% and 1.5%，and the probability of RMSE greater than 10% and PE greater than 6% was far less than 0.05. The study demonstrated that the robust delay compensation method can improve the accuracy of RTHS greatly and behavior strong robustness.