Genomic predictions across environments and within populations resulted in moderate to high accuracies but across-population genomic prediction should not be considered in wheat for small population size. Genomic selection (GS) is a marker-based selection suggested to improve the genetic gain of quantitative traits in plant breeding programs. We evaluated the effects of training population (TP) composition, cross-validation design, and genetic relationship between the training and breeding populations on the accuracy of GS in spring wheat (Triticum aestivum L.). Two populations of 231 and 304 spring hexaploid wheat lines that were phenotyped for six agronomic traits and genotyped with the wheat 90 K array were used to assess the accuracy of seven GS models (RR-BLUP, G-BLUP, BayesB, BL, RKHS, GS + de novo GWAS, and reaction norm) using different cross-validation designs. BayesB outperformed the other models for within-population genomic predictions in the presence of few quantitative trait loci (QTL) with large effects. However, including fixed-effect marker covariates gave better performance for an across-population prediction when the same QTL underlie traits in both populations. The accuracy of prediction was highly variable based on the cross-validation design, which suggests the importance to use a design that resembles the variation within a breeding program. Moderate to high accuracies were obtained when predictions were made within populations. In contrast, across-population genomic prediction accuracies were very low, suggesting that the evaluated models are not suitable for prediction across independent populations. On the other hand, across-environment prediction and forward prediction designs using the reaction norm model resulted in moderate to high accuracies, suggesting that GS can be applied in wheat to predict the performance of newly developed lines and lines in incomplete field trials.