The large-scale structure of the Universe is the direct consequence of its evolution over billions of years. The observations of this large-scale structure in terms of galaxy redshift surveys contain valuable cosmological information and in order to extract that information, we need to compare these observations to corresponding theory predictions from cosmological simulations, whose generation in itself is a very computationally intensive feat. This work uses deep convolutional neural networks to simulate the large-scale structure of the Universe and generate a typical cosmological simulation orders of magnitude faster than the standard N-body simulations within an accuracy of ~1% on the most common cosmological summary statistics. The most important feature of our model is that it extrapolates extremely well on universes with entirely different cosmologies than the one it has been trained on. The use of such an approach will be particularly useful in the near future to compare theory with predictions, to generate mock galaxy catalogs, to compute covariance matrices, and to optimize observational strategies.