Recent work concerning quantitative traits of interest has focused on selecting a small subset of single nucleotide polymorphisms (SNPs) from among the SNPs responsible for the phenotypic variation of the trait. When considered as covariates, the large number of variables (SNPs) and their association with those in close proximity pose challenges for variable selection. The features of sparsity and shrinkage of regression coefficients of the least absolute shrinkage and selection operator (LASSO) method appear attractive for SNP selection. Sparse partial least squares (SPLS) is also appealing as it combines the features of sparsity in subset selection and dimension reduction to handle correlations among SNPs. In this paper, we investigate application of the LASSO and SPLS methods for selecting SNPs that predict quantitative traits. We evaluate the performance of both methods with different criteria and under different scenarios using simulation studies. Results indicate that these methods can be effective in selecting SNPs that predict quantitative traits but are limited by some conditions. Both methods perform similarly overall but each exhibit advantages over the other in given situations. Both methods are applied to Canadian Holstein cattle data to compare their performance.