The absence of a sedimentary record on large cratonic areas often prevents the reconstruction of the history of their vertical movements. The Reguibat Rise, belonging to the West African Craton, is typically a large basement high, whose Meso-Cenozoic history is poorly known because of the extreme reduction of this sedimentary record. In this paper we present the first thermochronological data from the centre of the Reguibat Rise, and combine them with the geometry of the sedimentary formations in the adjoining Tindouf and Taoudeni basins situated north and south, respectively. Fission track analysis on apatite yields ages from 256 +/- 21 Ma to 139 +/- 8 Ma, and 120 +/- 10 Ma by (U Th)/He dating. Two competing scenarios are tested based on these data with thermal history modelling. We favour the scenario that includes a Late Jurassic/Early Cretaceous cooling of the samples, based on stratigraphical constraints and the thermochronological results. We then propose a new model for the evolution of this region and reveal the occurrence of a previously unknown major exhumation event at the Jurassic/Cretaceous transition accounting for the main present-day structures.