Paired multi-modality medical images, can provide complementary information to help physicians make more reasonable decisions than single modality medical images. But they are difficult to generate due to multiple factors in practice (e.g., time, cost, radiation dose).To address these problems, multi-modality medical image translation has aroused increasing research interest recently. However, the existing works mainly focus on translation effect of a whole image instead of a critical target area or Region of Interest (ROI), e.g., organ and so on. This leads to poor-quality translation of the localized target area which becomes blurry, deformed or even with extra unreasonable textures. In this paper, we propose a novel target-aware generative adversarial network called TarGAN, which is a generic multi-modality medical image translation model capable of (1) learning multi-modality medical image translation without relying on paired data, (2) enhancing quality of target area generation with the help of target area labels. The generator of TarGAN jointly learns mapping at two levels simultaneously -whole image translation mapping and target area translation mapping. These two mappings are interrelated through a proposed crossing loss. The experiments on both quantitative measures and qualitative evaluations demonstrate that TarGAN outperforms the state-of-the-art methods in all cases. Subsequent segmentation task is conducted to demonstrate effectiveness of synthetic images generated by TarGAN in a real-world application. Our code is available at https://github.com/2165998/TarGAN.