P300 potential is important to cognitive neuroscience research, and has also been widely applied in brain-computer interfaces (BCIs). To detect P300, many neural network models, including convolutional neural networks (CNNs), have achieved outstanding results. However, EEG signals are usually high-dimensional. Moreover, since collecting EEG signals is time-consuming and expensive, EEG datasets are typically small. Therefore, data-sparse regions usually exist within EEG dataset. However, most existing models compute predictions based on point-estimate. They cannot evaluate prediction uncertainty and tend to make overconfident decisions on samples located in data-sparse regions. Hence, their predictions are unreliable. To solve this problem, we propose a Bayesian convolutional neural network (BCNN) for P300 detection. The network places probability distributions over weights to capture model uncertainty. In prediction phase, a set of neural networks can be obtained by Monte Carlo sampling. Integrating the predictions of these networks implies ensembling. Therefore, the reliability of prediction can be improved. Experimental results demonstrate that BCNN can achieve better P300 detection performance than point-estimate networks. In addition, placing a prior distribution over the weight acts as a regularization technique. Experimental results show that it improves the robustness of BCNN to overfitting on small dataset. More importantly, with BCNN, both weight uncertainty and prediction uncertainty can be obtained. The weight uncertainty is then used to optimize the network through pruning, and the prediction uncertainty is applied to reject unreliable decisions so as to reduce detection error. Therefore, uncertainty modeling provides important information to further improve BCI systems.