As a crucial part of video compression, intra prediction utilizes local information of images to eliminate the redundancy in spatial domain. In both H.265/HEVC and H.266/VVC, multiple directional prediction modes are employed to find the texture trend of each small block and then the prediction is made based on reference samples in the selected direction. Recently, the intra prediction schemes based on neural networks have achieved great success. In these methods, the networks are trained and applied to intra prediction in addition to the directional prediction modes. In this paper, we propose a novel data clustering-driven neural network (dubbed DCDNN) for intra prediction, which can learn deep features of the clustered data. In DCDNN, each network can be split into two networks by adding or subtracting Gaussian random noise. Then a data clustering-driven training is applied to train all the derived networks recursively. In each iteration, the entire training dataset is partitioned according to the recovery qualities of the derived networks. For the experiment, DCDNN is implemented into HEVC reference software HM-16.9. The experimental results demonstrate that DCDNN can reach an average of 4.2% Bjontegaard distortion rate (BDrate) improvement (up to 7.0%) over HEVC with all intra configuration. Compared with existing fully connected networkbased intra prediction methods, the bitrate saving performance is further improved.