Seismic velocity is one of the most important parameters used in seismic exploration. Accurate velocity models are key prerequisites for reverse-time migration and other high-resolution seismic imaging techniques. Such velocity information has traditionally been derived by tomography or full-waveform inversion (FWI), which are time consuming and computationally expensive, and they rely heavily on human interaction and quality control. We investigate a novel method based on the supervised deep fully convolutional neural network (FCN) for velocity-model building (VMB) directly from raw seismograms. Unlike the conventional inversion method based on physical models, the supervised deep-learning methods are based on big-data training rather than prior-knowledge assumptions. During the training stage, the network establishes a nonlinear projection from the multi-shot seismic data to the corresponding velocity models. During the prediction stage, the trained network can be used to estimate the velocity models from the new input seismic data. One key characteristic of the deep-learning method is that it can automatically extract multi-layer useful features without the need for human-curated activities and initial velocity setup. The data-driven method usually requires more time during the training stage, and actual predictions take less time, with only seconds needed. Therefore, the computational time of geophysical inversions, including real-time inversions, can be dramatically reduced once a good generalized network is built. By using numerical experiments on synthetic models, the promising performances of our proposed method are shown in comparison with conventional FWI even when the input data are in more realistic scenarios. Discussions on the deep-learning methods, training dataset, lack of low frequencies, and advantages and disadvantages of the new method are also provided.