This paper proposes a self organizing RBF neural network equalizer for the equalization of digital communications. It is the most important for the equalizer using the RBF neural network to estimate the RBF centers correctly and quickly, which are the desired channel states. However, the previous RBF equalizers are not used in the actual communication system because of some drawbacks that the number of channel states has to be known in advance and many centers are necessary. Self organizing neural network equalizer proposed in this paper can implement the equalization without prior information regarding the number of channel states because it selects RBF centers among the signals that are transmitted to the equalizer by the new addition and removal criteria. Furthermore, the proposed equalizer has a merit that is able to make a equalization with fewer centers than those of prior one by the course of the training using LMS and clustering algorithm. In the linear, nonlinear and standard telephone channel, the proposed equalizer is compared with the optimal Bayesian equalizer for the BER performance, the symbol decision boundary and the number of centers. As a result of the comparison, we can confirm that the proposed equalizer has almost similar performance with the Bavesian enualizer.