A novel adaptive blind equalization method based on sparse Bayesian learning (blind relevance vector machine (RVM) equalizer) is proposed. This paper incorporates a Godard or constant modulus algorithm (CMA)-like error function into a general Bayesian framework. This Bayesian frame work can obtain sparse solutions to regression tasks utilizing models linear in the parameters. By exploiting a probabilistic Bayesian learning framework, the sparse Bayesian learning provides the accurate model for the blind equalization, which typically utilizes fewer basis functions than the equalizer based on the popular and state-of-the-art support vector machine (SVM) - blind SVM equalizer. Simulation results show that the proposed blind RVM equalizer provides improved stability, performance and complexity compared to the blind SVM equalizer in terms of inter-symbol interference and bit error rate.