The resistance of durum wheat to the Wheat spindle streak mosaic virus (WSSMV) is controlled by two main QTLs on chromosomes 7A and 7B, with a huge epistatic effect. Wheat spindle streak mosaic virus (WSSMV) is a major disease of durum wheat in Europe and North America. Breeding WSSMV-resistant cultivars is currently the only way to control the virus since no treatment is available. This paper reports studies of the inheritance of WSSMV resistance using two related durum wheat populations obtained by crossing two elite cultivars with a WSSMV-resistant emmer cultivar. In 2012 and 2015, 354 recombinant inbred lines (RIL) were phenotyped using visual notations, ELISA and qPCR and genotyped using locus targeted capture and sequencing. This allowed us to build a consensus genetic map of 8568 markers and identify three chromosomal regions involved in WSSMV resistance. Two major regions (located on chromosomes 7A and 7B) jointly explain, on the basis of epistatic interactions, up to 43% of the phenotypic variation. Flanking sequences of our genetic markers are provided to facilitate future marker-assisted selection of WSSMV-resistant cultivars.