Technical Abstract: Genomic selection (GS) is a promising approach to accelerate gain in plant breeding programs. In GS, genome-wide molecular markers are used to predict total breeding values and make selections of individuals or breeding lines prior to phenotyping. One premise of applying GS is that low-cost genome-wide molecular markers are readily available. Here we show that genotyping-by-sequencing (GBS) can be used for de novo genotyping of breeding panels and used to develop GS models, even for the large, complex, and polyploid wheat genome. Cross validation prediction accuracy with GBS was greater than an established marker platform and high enough to apply GS in breeding programs. We developed a novel multivariate normal expectation-maximization algorithm to impute markers in the GBS dataset and show that this algorithm has better performance for the unbiased imputation of sparse genotyping data in sequence-based genotyping when applied to genomic selection. As GBS combines marker discovery and genotyping of large populations it is an excellent marker platform for breeding applications even in the absence of any reference genome sequence or previous polymorphism discovery. Rapid advances in sequencing output will further decrease the cost of GBS; an ideal situation for applying GS in plant breeding programs.