In this talk, I will propose a new high-fidelity image compression method using optimal transport (OT) mapping to obtain high compression ratio while still preserving fine details about the image. First, I will briefly introduce the theory of OT mapping and how to combine generative adversarial network (GAN) with it to build a compression system. Then I will describe our proposed method. Experimental results show that our method has better performance under objective criteria than other GAN-based methods.