The recent availability of an assembled and annotated genome reference sequence for the diploid crop barley (Hordeum vulgare L.) provides new opportunities to study the genetic basis of agronomically important traits such as resistance to stripe [Puccinia striiformis f. sp. hordei (Psh)], leaf [P. hordei (Ph)], and stem [P. graminis f. sp. tritici (Pgt)] rust diseases. The European barley cultivar Pompadour is known to possess high levels of resistance to leaf rust, predominantly due to adult plant resistance (APR) gene Rph20. We developed a barley recombinant inbred line (RIL) population from a cross between Pompadour and the leaf rust and stripe rust susceptible selection Biosaline-19 (B-19), and genotyped this population using DArT-Seq genotyping by sequencing (GBS) markers. In the current study, we produced a high-density linkage map comprising 8,610 (SNP and in silico) markers spanning 5957.6 cM, with the aim of mapping loci for resistance to leaf rust, stem rust, and stripe rust. The RIL population was phenotyped in the field with Psh (Mexico and Ecuador) and Ph (Australia) and in the greenhouse at the seedling stage with Australian Ph and Pgt races, and at Wageningen University with a European variant of Psh race 24 (PshWUR). For Psh, we identified a consistent field QTL on chromosome 2H across all South American field sites and years. Two complementary resistance genes were mapped to chromosomes 1H and 4H at the seedling stage in response to PshWUR, likely to be the loci rpsEm1 and rpsEm2 previously reported from the cultivar Emir from which Pompadour was bred. For leaf rust, we determined that Rph20 in addition to two minor-effect QTL on 1H and 3H were effective at the seedling stage, whilst seedling resistance to stem rust was due to QTL on chromosomes 3H and 7H conferred by Pompadour and B-19, respectively.