This paper presents a wave-equation skeletonized inversion method to invert for the subsurface velocity model. The skeletonized data of the seismic trace is predicted by a well-trained autoencoder neural network. The implicit function theorem is used to connect the perturbation of the skeletonized data with respect to the velocity with the Frechet derivative (perturbation of seismogram with respect to the velocity). The gradient is computed by migrating the observed traces weighted by the residuals of the skeletonized data. The velocity model is perturbed until the skeletonized data predicted from the synthetic traces are best fit with the skeletonized data from the observed traces. The cycle-skipping problem has largely mitigated compared to the conventional full waveform inversion (FWI) method by avoiding the usage of the waveform difference. Numerical tests on both the synthetic and real data demonstrate the success of this skeletonized inversion method in recovering the subsurface velocity model. The disadvantage of this method is that the inverted velocity model has less resolution compared to the FWI result, but which can be a good initial model for FWI.