This paper proposes a rapid inverse analysis approach based on the reduced-basis method (RBM) and neural network (NN) to identify the "unknown" elastic modulus (Young's modulus) of the interfacial tissue between a dental implant and the surrounding bones. In the present RBM-NN approach, a RBM model is first built to compute displacement responses of dental implant-bone structures subjected to a harmonic loading for a set of "assumed" Young's moduli. The RBM model is then used to train a NN model that is used for actual inverse analysis in real-time. Actual experimental measurements of displacement responses are fed into the trained NN model to inversely determine the "true" elastic modulus of the interfacial tissue. As an example, a physical model of dental implant-bone structure is built and inverse analysis is conducted to verify the present RBM-NN approach. Based on numerical simulation and actual experiments, it is confirmed that the identified results are very accurate, reliable, and the computational saving is very significant. The present RBM-NN approach is found robust and efficient for inverse material characterizations in noninvasive and/or nondestructive evaluations.