In this paper, simulation was used to determine accuracies of genomic breeding values for polygenic traits associated with many thousands of markers obtained from high density genome scans. The statistical approach was based upon stochastically simulating a pedigree with a specified base population and a specified set of population parameters including the effective and noneffective marker distances and generation time. For this population, marker and quantitative trait locus (QTL) genotypes were generated using either a single linkage group or multiple linkage group model. Single nucleotide polymorphism (SNP) was simulated for an entire bovine genome (except for the sex chromosome, n = 29) including linkage and recombination. Individuals drawn from the simulated population with specified marker and QTL genotypes were randomly mated to establish appropriate levels of linkage disequilibrium for ten generations. Phenotype and genomic SNP data sets were obtained from individuals starting after two generations. Genetic prediction was accomplished by statistically modeling the genomic relationship matrix and standard BLUP methods. The effect of the number of linkage groups was also investigated to determine its influence on the accuracy of breeding values for genomic selection. When using high density scan data (0.08 cM marker distance), accuracies of breeding values on juveniles were obtained of 0.60 and 0.82, for a low heritable trait (0.10) and high heritable trait (0.50), respectively, in the single linkage group model. Estimates of 0.38 and 0.60 were obtained for the same cases in the multiple linkage group models. Unexpectedly, use of BLUP regression methods across many chromosomes was found to give rise to reduced accuracy in breeding value determination. The reasons for this remain a target for further research, but the role of Mendelian sampling may play a fundamental role in producing this effect.