A redundant electro-hydraulic shaking table (REST) of six degrees-of-freedom (6 DOFs) with eight hydraulic actuators is an essential experimental tool in many industrial applications for real-time simulation of actual vibrations, such as structural vibration, earthquake simulation and fatigue testing. In order to obtain a high-fidelity acceleration waveform on the REST, a feed-forward inverse model (FFIM) controller with a modelling error compensator is proposed in this study. A recursive extended least-squares algorithm is employed to identify an acceleration closed-loop transfer function of the REST. A zero phase error compensation technology is employed to guarantee stability of the designed FFIM because the identified acceleration closed-loop transfer function is a typical non-minimum phase system and its direct inverse transfer function is unstable. The modelling error compensator is designed to compensate for the modelling error between the identified transfer function and the actual experimental REST, which deteriorates the acceleration waveform replication accuracy of the REST. A 6 DOF REST experimental system was used to verify the proposed controller. Experimental results demonstrated that the proposed controller gave satisfactory acceleration tracking performances on the REST.