Most of the deep learning-based speech enhancement models are learned in a supervised manner, which implies that pairs of noisy and clean speech are required during training. Consequently, several noisy speeches recorded in daily life cannot be used to train the model. Although certain unsupervised learning frameworks have also been proposed to solve the pair constraint, they still require clean speech or noise for training. Therefore, in this paper, we propose MetricGAN-U, which stands for MetricGAN-unsupervised, to further release the constraint from conventional unsupervised learning. In MetricGAN-U, only noisy speech is required to train the model by optimizing non-intrusive speech quality metrics. The experimental results verified that MetricGAN-U outperforms baselines in both objective and subjective metrics.