Summary: Molecular markers combined with powerful statistical tools have made it possible to detect and analyze multiple loci on the genome that are responsible for the phenotypic variation in quantitative traits. The objectives of the study presented in this paper are to identify a subset of single nucleotide polymorphism (SNP) markers that are associated with a particular trait and to construct a model that can best predict the value of the trait given the genotypic information of the SNPs using a three-step strategy. In the first step, a genome-wide association test is performed to screen SNPs that are associated with the quantitative trait of interest. SNPs with \(p\)-values of less than 5% are then analyzed in the second step. In the second step, a large number of randomly selected models, each consisting of a fixed number of randomly selected SNPs, are analyzed using the least angle regression method. This step will further remove redundant SNPs due to the complicated association among SNPs. A subset of SNPs that are shown to have a significant effect on the response trait more often than by chance are considered for the third step. In the third step, two alternative methods are considered: the least angle shrinkage and selection operation and sparse partial least squares regression. For both methods, the predictive ability of the fitted model is evaluated by an independent test set. The performance of the proposed method is illustrated by the analysis of a real data set on Canadian Holstein cattle.