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Electro-hydraulic shake table (EHST) is vital seismic testing equipment in earthquake engineering for the assessment of structures subject to dynamic vibration excitations. The EHST system can be generally simplified as an electro-hydraulic servo system with prominent acceleration replication requirement. In order to improve the acceleration tracking performance of a typical EHST system, a novel real-time acceleration tracking strategy combining inverse compensation technique and neural-based adaptive controller is presented in this paper. The traditional three variable controller (TVC) is applied to the EHST system for obtaining a preliminary acceleration tracking accuracy in advance, and then the multi-innovation stochastic gradient algorithm is utilized to estimate the discrete parametric transfer function of the TVC controlled EHST system. Next, the zero magnitude error tracking technique, which is capable of handling non-minimum phase zeros, is exploited to design a stable and casual inverse model, and subsequently the parametric inverse compensation technique for the EHST system is constructed. Finally, a neural-based online adaptive controller is incorporated to the offline designed parametric inverse compensator as an outer loop, and the side effects of the system’s inherent nonlinearities, varying dynamics, and external uncertainties are further addressed. The proposed controller is successfully implemented in the control system of a unidirectional EHST test rig using xPC target rapid prototyping technique, and experimental results reveal that a superior acceleration replication performance is achieved in contrast to the other comparative controllers.