The genus Amaranthus consists of about 70 species and harbors several cultivated and weedy species of great economic importance. A lack of suitable traits, phenotypic plasticity, gene flow and hybridization made it difficult to establish the taxonomy and phylogeny of the whole genus despite various studies using molecular markers. We inferred the phylogeny of the Amaranthus genus using genotyping by sequencing (GBS) of 94 individuals from 35 Amaranthus and compared single nucleotide polymorphism (SNP) calling rates with reference-based and de novo methods. For reference-based SNP calling we used the distant sugarbeet Beta vulgaris and the closely related Amaranthus hypochondriacus as references, and in addition two different parameter sets for the de novo SNP calling. We obtained different numbers of SNPs and proportions of missing data, but the phylogenetic trees calculated from these data were very similar. We estimated a species tree for the genus using the multispecies coalescent. Both phylogenetic methods supported the taxonomic grouping into three subgenera although the subgenus A. Acnida consists of two highly differentiated clades. In contrast, the Hybridus complex within the A. Amaranthus subgenus that includes grain amaranths and their wild relatives was well separated from the other species. However, it was not differentiated into species but into geographic origin from South and Central America. Different geographically separated populations of Amaranthus hybridus appear to be the common ancestors of the three cultivated grain species and A. quitensis might be further involved in the evolution of South American grain amaranth (A. caudatus). We also measured genome sizes of the species and observed little variation with the exception of two lineages that showed evidence for a recent polyploidization.