By cross-matching the currently largest optical catalogue of galaxy clusters and the NVSS radio survey data base, we obtain a large complete sample of brightest cluster galaxies (BCGs) in the redshift range of 0.05<z<=0.45, which have radio emission and redshift information. We confirm that more powerful radio BCGs tend to be these optically very bright galaxies located in more relaxed clusters. We derived the radio luminosity functions of the largest sample of radio BCGs, and find that the functions depend on the optical luminosity of BCGs and the dynamic state of galaxy clusters. However, the radio luminosity function does not show significant evolution with redshift.