Leprosy is a chronic infectious disease of the skin and peripheral nerves with a strong genetic predisposition. Recent genome-wide approaches have identified numerous common variants associated with leprosy, almost all in the Chinese population. We conducted the first family-based genome-wide association study of leprosy in 622 affected offspring from Vietnam, followed by replication in an independent sample of 1181 leprosy cases and 668 controls of the same ethnic origin. The most significant results were observed within the HLA region, in which six SNPs displayed genome-wide significant associations, all of which were replicated in the independent case/control sample. We investigated the signal in the HLA region in more detail, by conducting a multivariate analysis on the case/control sample of 319 GWAS-suggestive HLA hits for which evidence for replication was obtained. We identified three independently associated SNPs, two located in the HLA class I region (rs1265048: OR = 0.69 [0.58-0.80], combined p-value = 5.53x10$^{-11}$; and rs114598080: OR = 1.47 [1.46-1.48], combined p-value = 8.77x10$^{-13}$), and one located in the HLA class II region (rs3187964 (OR = 1.67 [1.55-1.80], combined p-value = 8.35x10$^{-16}$). We also validated two previously identified risk factors for leprosy: the missense variant rs3764147 in the LACC1 gene (OR = 1.52 [1.41-1.63], combined p-value = 5.06x10$^{-14}$), and the intergenic variant rs6871626 located close to the IL12B gene (OR = 0.73 [0.61-0.84], combined p-value = 6.44x10$^{-8}$). These results shed new light on the genetic control of leprosy, by dissecting the influence of HLA SNPs, and validating the independent role of two additional variants in a large Vietnamese sample.