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During a real-time hybrid simulation (RTHS), inevitable time delay of actuators when responding to a command will reduce the accuracy of test results and sometimes even cause unstable testing. The inner-loop controller of an actuator is generally capable of eliminating the effects due to small time-delays. However, if a test specimen behaves nonlinearly, accuracy of RTHS results will be impaired. In addition to the uncertainty of test specimens and transfer system, measurement noises of the displacement and force sensors also require a robust external controller for RTHS. In this paper, a robust linear-quadratic-gaussian (LQG) controller with a Loop Transfer Recovery (LTR) procedure and a polynomial-based feedforward prediction (FP) algorithm is proposed to compensate the adverse effects due to time delay and uncertainties within the RTHS testing system. The stability and robustness of the proposed controller are analysed in the frequency domain using the Nyquist curve and the Bode diagrams. Numerical simulations are then carried out on the benchmark problem using both the proposed robust and the conventional LQG controllers and their performance is compared using the nine evaluation criteria. It is demonstrated that the robust LQG (RLQG) controller outperforms the conventional LQG controller in terms of compensating the parameter uncertainties in the testing system and achieving accurate RTHS results.