Traditional iteration-based full-waveform inversion (FWI) methods encounter serious challenges if the initial velocity model is far from the true model or if the observed data are lacking low-frequency content. As such, the optimization algorithm may be trapped in local minima and fail to go to a global optimal model. In addition, the traditional FWI method requires long-offset data to update the deep structure of a velocity model with diving waves. To overcome the disadvantages of traditional FWI under these circumstances, we have developed a reflection intensity waveform inversion method. This method aims to minimize the seismic intensity differences between the modeled reflection data and field data. Our method is less dependent on the starting model, and long-offset data are no longer required. The wave intensity, proportional to the square of the original data amplitude, can have a low-frequency band and a higher frequency band, even for waveforms without initial low-frequency content. Our multiscale intensity inversion starts from the low-frequency information in the intensity data, and it can largely avoid the cycle-skipping problem. Synthetic and field data examples demonstrate that our method is able to overcome cycle skipping in handling data with no low-frequency information.