Genome-wide assisted selection is a critical tool for the genetic improvement of plants and animals. Whole-genome regression models in Bayesian framework represent the main family of prediction methods. Fitting such models with a large number of observations involves a prohibitive computational burden. We propose the use of subsampling bootstrap Markov chain in genomic prediction. Such method consists of fitting whole-genome regression models by subsampling observations in each round of a Markov Chain Monte Carlo. We evaluated the effect of subsampling bootstrap on prediction and computational parameters.