In this paper, we propose a quasi-periodic parallel WaveGAN (QPPWG) waveform generative model, which applies a quasi-periodic (QP) structure to a parallel WaveGAN (PWG) model using pitch-dependent dilated convolution networks (PD-CNNs). PWG is a small-footprint GAN-based raw waveform generative model, whose generation time is much faster than real time because of its compact model and non-autoregressive (non-AR) and non-causal mechanisms. Although PWG achieves high-fidelity speech generation, the generic and simple network architecture lacks pitch controllability for an unseen auxiliary fundamental frequency (F0) feature such as a scaled F0. To improve the pitch controllability and speech modeling capability, we apply a QP structure with PDCNNs to PWG, which introduces pitch information to the network by dynamically changing the network architecture corresponding to the auxiliary F0 feature. Both objective and subjective experimental results show that QP-PWG outperforms PWG when the auxiliary F0 feature is scaled. Moreover, analyses of the intermediate outputs of QPPWG also show better tractability and interpretability of QPPWG, which respectively models spectral and excitation-like signals using the cascaded fixed and adaptive blocks of the QP structure. Index Terms-Neural vocoder, parallel WaveGAN, quasiperiodic WaveNet, pitch-dependent dilated convolution I. INTRODUCTION S PEECH generation is a technique to generate specific speech according to given inputs such as texts (text-tospeech, TTS), the speech of a source speaker (speaker voice conversion, VC), and noisy speech (speech enhancement, SE). The core of speech generation is the controllability of speech components, and the fundamental technique is called a vocoder [1]-[3]. A vocoder encodes speech into acoustic Manuscript received xxx xx, 2020; revised xxx xx, 2020.