The outbreak of COVID-19 Disease due to the novel coronavirus has caused a shortage of medical resources . To aid and accelerate the diagnosis process, automatic diagnosis of COVID-19 via deep learning models has recently been explored by researchers across the world . While different data-driven deep learning models have been developed to mitigate the diagnosis of COVID-19, the data itself is still scarce due to patient privacy concerns . Federated Learning (FL) is a natural solution because it allows different organizations to cooperatively learn an effective deep learning model without sharing raw data . However, recent studies show that FL still lacks privacy protection and may cause data leakage . We investigate this challenging problem by proposing a simple yet effective algorithm, named \textbf {F} ederated \textbf {L} earning \textbf {o} n Medical Datasets using \textbf {P} artial Networks (FLOP), that shares only a partial model between the server and clients . Extensive experiments on benchmark data and real-world healthcare tasks show that our approach achieves comparable or better performance while reducing the privacy and security risks . Of particular interest, we conduct experiments on the COVID-19 dataset and find that our FLOP algorithm can allow different hospitals to collaboratively and effectively train a partially shared model without sharing local patients' data.