Genomic prediction (GP) has become a valuable tool for predicting the performance of selection candidates for the next breeding cycle. A vast majority of statistical linear models on which GP is based rely on the assumption of normality of the residuals and therefore on the response variable itself. In this study, we propose to use Bayesian regularized quantile regression (BRQR) in the context of GP; the model has been successfully used in other research areas. We evaluated the prediction ability of the proposed model and compared it with the Bayesian ridge regression (BRR; equivalent to genomic best linear unbiased predictor, GBLUP). In addition, BLUP can be used with pedigree information obtained from the coefficient of coancestry (ABLUP). We have found that the prediction ability of BRQR is comparable to that of BRR and, in some cases, better;it also has the potential to efficiently deal with outliers. A program written in the R statistical package is available as Supplementary material.