The Southern Ocean hosts an abundant and diverse fauna. The evolutionary history of these taxa has been strongly influenced by the oceanographic and glacial history of this region. Molecular studies have challenged the traditional characterization of many Antarctic taxa as circumpolar, uncovering large amounts of unexpected diversity. In this study,we investigate the genetic diversity and population structuring of G. antarctica. Using double digest restriction-site associated DNA sequencing, we obtain a set of 4301 SNP markers from across the genome for a set of four populations spanning a large portion of this taxa's range distribution. This data set reveals clear evidence of strong population structuring across the Southern Ocean, at both large and small geographic scales. We reject the hypothesis of panmixia within the geographic region investigated. The data presents evidence of the influence of both the Antarctic Circumpolar Current and the last glacial maximum on the genetic structure of G. antarctica