Speech enhancement aims to obtain speech signals with high intelligibility and quality from noisy speech. Recent work has demonstrated the excellent performance of time-domain deep learning methods, such as Conv-TasNet. However, these methods can be degraded by the arbitrary scales of the waveform induced by the scale-invariant signal-to-noise ratio (SI-SNR) loss. This paper proposes a new framework called Timedomain Speech Enhancement Generative Adversarial Network (TSEGAN), which is an extension of the generative adversarial network (GAN) in time-domain with metric evaluation to mitigate the scaling problem, and provide model training stability, thus achieving performance improvement. In addition, we provide a new method based on objective function mapping for the theoretical analysis of the performance of Metric GAN, and explain why it is better than the Wasserstein GAN. Experiments conducted demonstrate the effectiveness of our proposed method, and illustrate the advantage of Metric GAN.