Numerous marine applications require the prediction of medium- and long-term sea states. Climate models are mainly focused on the description of the atmosphere and global ocean variables, most often on a synoptic scale. Downscaling models exist to move from these atmospheric variables to the integral descriptors of the surface state; however, they are most often complex numerical models based on physics equations that entail significant computational costs. Statistical downscaling models provide an alternative to these models by constructing an empirical relationship between large-scale atmospheric variables and local variables, using historical data. Among the existing methods, deep learning methods are attracting increasing interest because of their ability to build hierarchical representations of features. To our knowledge, these models have not yet been tested in the case of sea state downscaling. In this study, a convolutional neural network (CNN)-type model for the prediction of significant wave height from wind fields in the Bay of Biscay is presented. The performance of this model is evaluated at several points and compared to other statistical downscaling methods and to WAVEWATCH III hindcast databases. The results obtained from these different stations show that the proposed method is suitable for predicting sea states. The observed performances are superior to those of the other statistical downscaling methods studied but remain inferior to those of the physical models. The low computational cost and the ease of implementation are, however, important assets for this method.