Species distribution models (SDM) are widely used for ecological research and conservation purposes. Given a set of species occurrence, the aim is to infer its spatial distribution over a given territory. Because of the limited number of occurrences of specimens, this is usually achieved through environmental niche modeling approaches, i.e. by predicting the distribution in the geographic space on the basis of a mathematical representation of their known distribution in environmental space (= realized ecological niche). The environment is in most cases represented by climate data (such as temperature, and precipitation), but other variables such as soil type or land cover can also be used. In this paper, we propose a deep learning approach to the problem in order to improve the predictive effectiveness. Non-linear prediction models have been of interest for SDM for more than a decade but our study is the first one bringing empirical evidence that deep, convolutional and multilabel models might participate to resolve the limitations of SDM. Indeed, the main challenge is that the realized ecological niche is often very different from the theoretical fundamental niche, due to environment perturbation history, species propagation constraints and biotic interactions. Thus, the realized abundance in the environmental feature space can have a very irregular shape that can be difficult to capture with classical models. Deep neural networks on the other side, have been shown to be able to learn complex non-linear transformations in a wide variety of domains. Moreover, spatial patterns in environmental variables often contains useful information for species distribution but are usually not considered in classical models. Our study shows empirically how convolutional neural networks efficiently use this information and improve prediction performance.