In seismic exploration, identifying the first break (FB) is a critical component in establishing subsurface velocity models. Various automatic picking techniques based on deep neural networks have been developed to expedite this procedure. The most popular class is using semantic segmentation networks to pick on a shot gather called 2-dimensional (2-D) picking. Generally, 2-D segmentation-based picking methods input an image of a shot gather, and output a binary segmentation map, in which the maximum of each column is the location of FB. However, current designed segmentation networks is difficult to ensure the horizontal continuity of the segmentation. Additionally, FB jumps also exist in some areas, and it is not easy for current networks to detect such jumps. Therefore, it is important to pick as much as possible and ensure horizontal continuity. To alleviate this problem, we propose a novel semantic segmentation network for the 2-D seismic FB picking task, where we introduce the dynamic snake convolution into U-Net and call the new segmentation network dynamic-snake U-Net (DSU-Net). Specifically, we develop original dynamic-snake convolution (DSConv) in CV and propose a novel DSConv module, which can extract the horizontal continuous feature in the shallow feature of the shot gather. Many experiments have shown that DSU-Net demonstrates higher accuracy and robustness than the other 2-D segmentation-based models, achieving state-of-the-art (SOTA) performance in 2-D seismic field surveys. Particularly, it can effectively detect FB jumps and better ensure the horizontal continuity of FB. In addition, the ablation experiment and the anti-noise experiment, respectively, verify the optimal structure of the DSConv module and the robustness of the picking.