Genetic analysis of discrete traits such as litter size or mortality of livestock has been studied using generalized linear mixed model employing a discrete distribution. Recently, genome-wide dense SNP marker information is available in animal breeding to predict genome-wide breeding values. The objectives of this study were to develop Bayesian hierarchical Poisson and binomial models for predicting genome-wide breeding values of discrete traits and to compare these two models for the accuracy of the prediction. A t-distribution was used as prior of all SNP effects in the models, which was the so-called BayesA setting. The prediction accuracy was evaluated using simulated data and actual behavior traits of heterogeneous stock mouse. In the analysis of simulated data, where observed trait in each animal followed a Poisson distribution with the logarithm of its parameter expressed as a linear combination of 50 or 1,000 additive QTL effects, both the hierarchical models gave similar accuracy of prediction, but the Poisson model performed slightly better then the binomial in mean-squared error between observed and predicted phenotypes. The hierarchical binomial model had some advantages in the predictive ability over the Poisson model when analyzing the open field activity of heterogeneous stock mouse (2 levels). The results of this study suggest that the Bayesian hierarchical models seem a reasonable choice for predicting genomic-wide breeding value of discrete traits.