A complete sample of 18 X-ray selected clusters of galaxies belonging to the ROSAT North Ecliptic Pole (NEP) survey has been observed with the Very Large Array at 1.4GHz in B configuration. These are the most distant clusters in the X-ray survey with redshift in the range 0.3<z<0.8. Seventy-nine radio sources are detected within half an Abell radius with an observed peak brightness >=0.17mJy/beam, except for three sources, belonging to the same cluster, which have a higher peak brightness limit of 0.26mJy/beam. The NEP field source counts are in good agreement with the source counts of a comparison survey, the VLA-VIRMOS deep field survey, indicating that the NEP sample is statistically complete. Thirty-two out of the 79 sources are within 0.2 Abell radii, twenty-two of them are considered cluster members based on spectroscopic redshifts or their optical magnitude and morphological classification. The cluster radio galaxies are used to construct the Radio Luminosity Function (RLF) of distant X-ray selected clusters. A comparison with two nearby cluster RLFs shows that the NEP RLF lies above the local ones, has a steeper slope at low radio powers (<=10^24^W/Hz) and shows no evidence for a break at about 6x10^24^W/Hz which is observed in the nearby cluster RLFs. We discuss briefly the origin and possible explanations of the differences observed in the radio properties of nearby and distant clusters of galaxies. The main result of this study is that the RLF of the distant X-ray clusters is very different from that of the local rich Abell clusters.