Coronavirus disease 2019 (COVID-19) is a Public Health Emergency of International Concern infecting more than 40 million people across 188 countries and territories. Chest computed tomography (CT) imaging technique benefits from its high diagnostic accuracy and robustness, it has become an indispensable way for COVID-19 mass testing. Recently, deep learning approaches have become an effective tool for automatic screening of medical images, and it is also being considered for COVID-19 diagnosis. However, the high infection risk involved with COVID-19 leads to relative sparseness of collected labeled data limiting the performance of such methodologies. Moreover, accurately labeling CT images require expertise of radiologists making the process expensive and time-consuming. In order to tackle the above issues, we propose a supervised domain adaption based COVID-19 CT diagnostic method which can perform effectively when only a small samples of labeled CT scans are available. To compensate for the sparseness of labeled data, the proposed method utilizes a large amount of synthetic COVID-19 CT images and adjusts the networks from the source domain (synthetic data) to the target domain (real data) with a cross-domain training mechanism. Experimental results show that the proposed method achieves state-of-the-art performance on few-shot COVID-19 CT imaging based diagnostic tasks.