An extensive survey of the standing genetic variation in natural populations is among the priority steps in developing a species into a model system. In recent years, green foxtail (Setaria viridis), along with its domesticated form foxtail millet (S. italica), has rapidly become a promising new model system for C4 grasses and bioenergy crops, due to its rapid life cycle, large amount of seed production, and small diploid genome, among other characters. However, remarkably little is known about the genetic diversity in natural populations of this species. In this study, we survey the genetic diversity of a world-wide sample of more than 200 S. viridis accessions, using the genotyping by sequencing technique. Two distinct genetic groups in S. viridis and a third group resembling S. italica were identified, with considerable admixture among the three groups. We find the genetic variation of North American S. viridis correlates with both geography and climate, and is representative of the total genetic diversity in this species. This pattern may reflect several introduction/dispersal events of S. viridis into North America. We also modeled demographic history and show signal of recent population decline in one subgroup. Finally we show linkage disequilibrium decay is rapid (less then 45 kb) in our total sample and slow in genetic subgroups. These results together provide an in-depth understanding of the pattern of genetic diversity of this new model species on a broad geographic scale. They also provide key guidelines for on-going and future work including germplasm preservation, local adaptation, crossing designs and genome-wide association studies.