Seismic full-waveform inversion (FWI), which applies iterative methods to estimate high-resolution subsurface detail from seismograms, is a powerful imaging technique in exploration geophysics. In recent years the computational cost of FWI has grown exponentially due to the increasing size and resolution of seismic data. Moreover, it is a non-convex problem, and can become stuck in a local minima due to the limited accuracy of the initial velocity maps, the absence of low frequencies in the measurements, the presence of noise, and the approximate modeling of the wave-physics complexity. To overcome these computational issues, we develop a multiscale data-driven FWI method based on the fully convolutional network (FCN). In preparing the training data, we first develop a real-time style transform method to create a large set of physically realistic subsurface velocity maps from natural images. We then develop two convolutional neural networks with encoder-decoder structure to reconstruct the low- and high-frequency components of the subsurface velocity maps, respectively. To validate the performance of our new data-driven inversion method and the effectiveness of the synthesized training set, we compare it with conventional physics-based waveform inversion approaches using both synthetic and field data. These numerical results demonstrate that, once our model is fully trained, it can significantly reduce the computation time, and yield more accurate subsurface velocity map in comparison with conventional FWI.