This paper proposes a Perceptual Learned Video Compression (PLVC) approach with recurrent conditional GAN. We employ the recurrent auto-encoder-based compression network as the generator, and most importantly, we propose a recurrent conditional discriminator, which judges raw vs. compressed video conditioned on both spatial and temporal features, including the latent representation, temporal motion and hidden states in recurrent cells. This way, the adversarial training pushes the generated video to be not only spatially photo-realistic but also temporally consistent with the groundtruth and coherent among video frames. The experimental results show that the learned PLVC model compresses video with good perceptual quality at low bit-rate, and that it outperforms the official HEVC test model (HM 16.20) and the existing learned video compression approaches for several perceptual quality metrics and user studies. The project page is available at https://github.com/RenYang-home/PLVC.