Convolutional neural networks (CNNs) are being used in various fields related to image recognition and are achieving high recognition accuracy. However, most existing CNNs do not consider uncertainty in their predictions; that is, they do not account for the difficulty of prediction, and the extent to which their predictions are reliable is unclear. This problem is considered to be the cause of erroneous decisions when we use CNNs in practice. By considering the uncertainty of the prediction result, it is thought that recognition accuracy would improve, and erroneous decisions would be suppressed. We propose a Bayesian attention branch network (Bayesian ABN) that incorporates uncertainty into an attention branch network (ABN). The method incorporates a Bayesian neural network (Bayesian NN) into the ABN to account for uncertainty in the prediction result. Also, it outputs prediction results from two branches and chooses the one having the lower uncertainty. In evaluations using standard object recognition datasets, we confirmed that the proposed method improves the accuracy and reliability of CNNs.