Nowadays, with the rapid spread of Corona Virus Disease 2019 (COVID-19), this epidemic has become a threatening risk for global public health. Medical workers and researchers all over the world are struggling against the novel coronavirus in the front line. Because the computed tomography (CT) images from infected patients exposure characteristic abnormalities, automatic CT analyzers based on AI-based algorithms are extensively employed as effective weapons to aid clinicians. However, unbalanced data and lack of annotations obstruct AI-based algorithms applying in aided diagnosis because of their low performance. Therefore, in order to solve the above problems, a general-purpose solution is proposed to synthesize COVID-19 CT scans from non-COVID-19 data for providing high-quality negative-positive paired CT scans. Particularly, we introduce an elastic registration algorithm of CT images to manufacture paired training data. Then, a conditional Generative Adversarial Networks (GANs) based image-to-image translation model is implemented to synthesize COVID-19 CT scans from non-COVID-19 data. The effectiveness of our proposed algorithm used in COVID-19 aided diagnosis is verified in the experiments, and the identification and detection capacities of the classification models have been enhanced with the generated CT scans. Specifically, the precise lesion location is achieved by the generated data with a weakly supervised algorithm of class activation mapping (CAM). The model and code of this paper are publicly available at https://github.com/lihengbit/Synthesis-of-COVID-19-CT-Scan.