The current shortage and inefficient use of the frequency spectrum lead researchers to seek technological solutions to this problem [1], thus Cognitive Radio (CR) [2] is proposed, allowing a more efficient management of the existing resources so they can be exploited opportunistically by cognitive users.This paper presents the design and use of a Bayesian network for the characterization of the primary user (PU) in wireless networks (GSM 824.9 MHz) in order to generate a PU activity predictor, which could serve to the central entity of a cognitive network in making spectral decisions.From the results found, it is concluded that the artificial intelligence technique based on Bayesian networks allows to model and predict the behavior of the primary user above 80% for short future lapses of time.