Whole genome prediction models are useful tools for breeders when selecting candidate individuals early in life for rapid genetic gains. However, most prediction models developed so far assume that the response variable is continuous and that its empirical distribution can be approximated by a Gaussian model. A few models have been developed for ordered categorical phenotypes, but there is a lack of genomic prediction models for count data. There are well-established regression models for count data that cannot be used for genomic-enabled prediction because they were developed for a large sample size (n) and a small number of parameters (p); however, the rule in genomic-enabled prediction is that p is much larger than the sample size n. Here we propose a Bayesian mixed negative binomial (BMNB) regression model for counts, and we present the conditional distributions necessary to efficiently implement a Gibbs sampler. The proposed Bayesian inference can be implemented routinely. We evaluated the proposed BMNB model together with a Poisson model, a Normal model with untransformed response, and a Normal model with transformed response using a logarithm, and applied them to two real wheat datasets from the International Maize and Wheat Improvement Center. Based on the criteria used for assessing genomic prediction accuracy, results indicated that the BMNB model is a viable alternative for analyzing count data.