Seismic waves generated by meteoroid impacts have been detected by the Apollo lunar seismic network. These waves are sensitive to the crustal structure beneath both the seismic stations and the impact sites. We use a Markov chain Monte-Carlo algorithm in order to invert for lateral variations of crustal thickness on the Moon. The inversion uses travel times of seismic waves originating from multiple meteoroid impact locations. Previous seismic investigations constrained the crustal thickness solely for Apollo stations 12, 14 and 16, whereas our approach enables to estimate the crustal thickness at locations far from the Apollo network, and to build a first crustal thickness map based on seismic data. Here we compare our crustal thickness estimates based on seismic travel times to those based on inversions of the topography and gravity field. Both methods turn out to be coherent in the sense that highland sites possess a thicker crust than mare sites.