Positron emission topography (PET) has been substantially used in recent years. To minimize the potential health risks caused by the tracer radiation inherent to PET scans, it is of great interest to synthesize the high-quality full-dose PET image from the low-dose one to reduce the radiation exposure while maintaining the image quality. In this paper, we propose a locality adaptive multi-modality generative adversarial networks model (LA-GANs) to synthesize the full-dose PET image from both the low-dose one and the accompanying T1-weighted MRI to incorporate anatomical information for better PET image synthesis. This paper has the following contributions. First, we propose a new mechanism to fuse multi-modality information in deep neural networks. Different from the traditional methods that treat each image modality as an input channel and apply the same kernel to convolute the whole image, we argue that the contributions of different modalities could vary at different image locations, and therefore a unified kernel for a whole image is not appropriate. To address this issue, we propose a method that is locality adaptive for multi-modality fusion. Second, to learn this locality adaptive fusion, we utilize 1 × 1 × 1 kernel so that the number of additional parameters incurred by our method is kept minimum. This also naturally produces a fused image which acts as a pseudo input for the subsequent learning stages. Third, the proposed locality adaptive fusion mechanism is learned jointly with the PET image synthesis in an end-to-end trained 3D conditional GANs model developed by us. Our 3D GANs model generates high quality PET images by employing large-sized image patches and hierarchical features. Experimental results show that our method outperforms the traditional multi-modality fusion methods used in deep networks, as well as the state-of-the-art PET estimation approaches.