Unsupervised representation learning has shown remarkable achievement by reducing the performance gap with supervised feature learning, especially in the image domain. In this study, to extend the technique of unsupervised learning to the speech domain, we propose the Momentum Contrast for VoxCeleb (MoCoVox) as a form of learning mechanism. We pre-trained the MoCoVox on the VoxCeleb1 by implementing instance discrimination. Applying MoCoVox for speaker verification revealed that it outperforms the state-of-the-art metric learning-based approach by a large margin. We also empirically demonstrate the features of contrastive learning in the speech domain by analyzing the distribution of learned representations. Furthermore, we explored which pretext task is adequate for speaker verification. We expect that learning speaker representation without human supervision helps to address the open-set speaker recognition.