The equivalent force control method uses feedback control to replace numerical iteration and solve the nonlinear equation in a real-time hybrid simulation via the implicit integration method. During the real-time hybrid simulation, a time delay typically reduces the accuracy of the test results and can even make the system unstable. The outer-loop controller of the equivalent force control method can eliminate the effect of a small time delay. However, when the actuator has a large delay, the accuracy of the test results is reduced. The adaptive forward prediction method offers a solution to this problem. Thus, in this paper, the adaptive polynomial-based forward prediction algorithm is combined with equivalent force control to improve the test accuracy and stability. The new method is shown to give good stability properties for a specimen with nonlinear stiffness by analyzing the location of the poles of the discrete transfer system. Simulations with linear and nonlinear specimens are then presented to demonstrate the effectiveness of this method. Finally, experimental results with a linear stiffness specimen and a magneto-rheological damper are used to demonstrate that this method has better accuracy than the equivalent force control method with nonadaptive delay compensation.