In exploration geophysics, the first arrivals on data acquired under complicated near-surface conditions are often characterized by significant static corrections, weak energy, low signal-to-noise ratio, and dramatic phase change, and they are difficult to pick accurately with traditional automatic procedures. We have approached this problem by using a U-shaped fully convolutional network (U-net) to first-arrival picking, which is formulated as a binary segmentation problem. U-net has the ability to recognize inherent patterns of the first arrivals by combining attributes of arrivals in space and time on data of varying quality. An effective workflow based on U-net is presented for fast and accurate picking. A set of seismic waveform data and their corresponding first-arrival times are used to train the network in a supervised learning approach, then the trained model is used to detect the first arrivals for other seismic data. Our method is applied on one synthetic data set and three field data sets of low quality to identify the first arrivals. Results indicate that U-net only needs a few annotated samples for learning and is able to efficiently detect first-arrival times with high precision on complicated seismic data from a large survey. With the increasing training data of various first arrivals, a trained U-net has the potential to directly identify the first arrivals on new seismic data.