Sweetpotato (Ipomoea batatas) is an autohexaploid species with 90 chromosomes (2n = 6x = 90) and a basic chromosome number of 15, and is therefore regarded as one of the most challenging species for high-density genetic map construction. Here, we used single nucleotide polymorphisms (SNPs) identified by double-digest restriction site-associated DNA sequencing based on next-generation sequencing technology to construct a map for sweetpotato. We then aligned the sequence reads onto the reference genome sequence of I. trifida, a likely diploid ancestor of sweetpotato, to detect SNPs. In addition, to simplify analysis of the complex genetic mode of autohexaploidy, we used an S1 mapping population derived from self-pollination of a single parent. As a result, 28,087 double-simplex SNPs showing a Mendelian segregation ratio in the S1 progeny could be mapped onto 96 linkage groups (LGs), covering a total distance of 33,020.4 cM. Based on the positions of the SNPs on the I. trifida genome, the LGs were classified into 15 groups, each with roughly six LGs and six small extra groups. The molecular genetic techniques used in this study are applicable to high-density mapping of other polyploid plant species, including important crops.