In seismic exploration, the selection of first break times is a crucial aspect in the determination of subsurface velocity models, which in turn significantly influences the placement of wells. Many deep neural network (DNN)-based automatic first break picking methods have been proposed to speed up this picking processing. However, there has been no work on the uncertainty of the first picking results of the output of DNN. In this paper, we propose a new framework for first break picking based on a Bayesian neural network to further explain the uncertainty of the output. In a large number of experiments, we evaluate that the proposed method has better accuracy and robustness than the deterministic DNN-based model. In addition, we also verify that the uncertainty of measurement is meaningful, which can provide a reference for human decision-making.