The iterative wave-equation dispersion inversion can suffer from the local minimum problem when inverting seismic data from complex Earth models. We develop a multiscale, layerstripping method to alleviate the local minimum problem ofwave-equation dispersion inversion of Rayleigh waves and improve the inversion robustness. We first invert the high-frequency and near-offset data for the shallow S-velocity model, and gradually incorporate the lowerfrequency components of data with longer offsets to reconstruct the deeper regions of the model. We use a synthetic model to illustrate the local minima problem of wave-equation dispersion inversion and how our multiscale and layer-stripping wave-equation dispersion inversion method can mitigate the problem. We demonstrate the efficacy of our new method using field Rayleigh-wave data.