This paper proposes a WaveNet-based delay-free adaptive differential pulse code modulation (ADPCM) speech coding system. The WaveNet generative model, which is a stateof-the-art model for neural-network-based speech waveform synthesis, is used as the adaptive predictor in ADPCM. To further improve speech quality, mel-cepstrum-based noise shaping and postfiltering were integrated with the proposed ADPCM system. Both objective and subjective evaluation results indicate that the proposed ADPCM system outperformed not only the conventional ADPCM system based on ITU-T Recommendation G.726 but also the ADPCM system based on adaptive mel-cepstral analysis.