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Cognitive Radio (CR) technology enables secondary users (SUs) to opportunistically access unused licensed spectrum owned by the primary users (PUs). Therefore, it can potentially significantly enhance communication capacity, and hence is very encouraging in aerospace communications and deserve thorough study. One of the key problems in cognitive aerospace communications is to determine spectrum availability. In the past, many researchers have proposed to employ spectrum sensing to address this issue, which, however, consumes considerable energy and time. In this paper, we develop a deep learning system to predict spectrum availability, which does not require a priori knowledge of the activities of PUs. The performance of the proposed system is analyzed through extensive simulations.