Wind turbine simulator (WTS) is an important test rig for validating the control strategies of wind turbines (WT). Since the inertia of WTSs is much smaller than that of WTs, the inertia compensation scheme is usually employed in WTSs for replicating the slow mechanical behavior of WTs. In this paper, it is found that the instability of WTSs applying the inertia compensation scheme, characterized by the oscillation of compensation torque, is caused by the one-step time delay produced in the acceleration observation. Hence, a linear discrete model of WTS considering the time delay of acceleration observation is developed and its stability is analyzed. Moreover, in order to stably simulate WTs with large inertia, an improved inertia compensation scheme, applying a first-order digital filter to mitigate deviation response induced by the time delay, is proposed. And, the criterion for selecting the filter coefficients is established based on the stability condition analysis. Finally, the WTS with the proposed scheme is validated by simulations and experiments.