We present an improved crustal Vs model and Moho depth map using ambient noise wave-equation tomography. The so-called 'ambient noise wave-equation tomography' is a method to invert seismic ambient noise phase dispersion data based on elastic waveform simulation, which accounts for 3-D and finite frequency effects. We use cross-correlations of up to four years of continuous vertical-component ambient seismic noise recordings from 304 high-quality broadband stations in the Alpine region. We use model LSP_Eucrust1.0 obtained from traditional ambient noise tomography as initial model, and we iteratively improve the initial model by minimizing frequency-dependent phase traveltime differences between the observed and synthetic waveforms of Rayleigh waves in the period range 10-50 s. We obtain the final model after 15 iterations with ∼65% total misfit reduction compared to the initial model. At crustal depth, the final model significantly enhances the amplitudes and adjusts the shapes of velocity anomalies. At Moho and upper mantle depth, the final model corrects an obvious systematic velocity shift of the initial model. The resulting iso-velocity Moho map confirms a Moho step along the external side of the external crystalline massifs of the Northwestern Alps and reveals underplated gabbroic plutons in the lower most crust of the Central and Eastern Alps. Ambient noise wave-equation tomography turns out to be a useful tool to refine shear-wave velocity models obtained by traditional ambient noise tomography based on ray theory.