Technical Abstract: Genomic selection predicts genetic values with genome-wide markers. It is rapidly emerging in plant breeding and is widely implemented in animal breeding. Genetic correlations between quantitative traits are pervasive in many breeding programs. These correlations indicate that measurements of one trait carry information on another trait. Current univariate genomic selection on a single trait does not take advantage of this information. Multivariate genomic selection on multiple traits could accomplish this but has been little explored and tested in practical breeding programs. In this study, three multivariate linear models (i.e. BLUP, BayesA and BayesCp) were compared using simulated quantitative traits controlled by different genetic architectures. We also contrasted a conventional Bayesian shrinkage method (BayesA) with fixed hyper-parameters wit a full Bayesian modeling with estimated hyper-parametes. We found that optimal priors depended on the genetic architecture of the trait so that estimating them was beneficial. Importantly, we show in both simulated and real breeding data that the prediction accuracy for a low heritability trait can be significantly increased (e.g. > 40 percent) by multivariate genomic selection when a correlated high heritability trait is available. Factors affecting the performance of multiple trait genomic selection were explored. The impacts of multivariate genomic selection on index selection of multiple traits and single trait selection under multiple environments were discussed.