Physics-driven computational techniques, which suffer from ill-posedness and high computational cost, have long been the standard for solving full-waveform inversion. In this work, we develop a novel inversion technique that combines physicsdriven models with data-driven methodologies based on the fully convolutional neural network (FCN) architecture. We design a cycle-consistency loss to connect two FCN networks that are trained to incorporate both seismic forward and inverse modeling. To evaluate the performance of our new inversion technique, we conduct several experiments to compare our hybrid inversion method with pure data-driven techniques. The results show that our new methods significantly improve the performance by stabilizing the convergence of the training process, and therefore yield a higher inversion accuracy.