Genomic selection describes a selection strategy based on genomic breeding values predicted from dense single nucleotide polymorphism (SNP) data. Multiple methods have been proposed but the critical issue is how to decide whether an SNP should be included in the predictive set to estimate breeding values. One major disadvantage of the traditional Bayes B approach is its high computational demands caused by the changing dimensionality of the models. The use of stochastic search variable selection (SSVS) retains the same assumptions about the distribution of SNP effects as Bayes B, while maintaining constant dimensionality. When Bayesian SSVS was used to predict genomic breeding values for real dairy data over a range of traits it produced accuracies higher or equivalent to other genomic selection methods with significantly decreased computational and time demands than Bayes B.