The objective of this study is to identify a subset of SNPs from a genome-wide dense panel of SNPs to predict the estimated breeding values (EBVs) of bulls. This requires selecting variables from a high-dimensional variable space (thousands of SNPs) with a much smaller sample size (hundreds of available animals). In this thesis, a two-step variable selection strategy is proposed to tackle this problem. In the first step, 10,000 randomly selected models were analyzed using the least angle regression (LARS) method. A subset of SNPs that were found to have significant effects on the EBVs among the 10,000 randomly selected models would be considered as the input SNPs for the second step. In the second step, the least absolute shrinkage and selection operation (LASSO) variable selection method was used to obtain a final model for predicting the EBVs. In addition, the sparse partial least squares (SPLS) method was considered in the place of the LASSO. The performances of the LASSO and SPLS were compared.