Edge intelligent computing is widely used in the fields, such as the Internet of Medical Things (IoMT), which has advantages, including high data processing efficiency, strong real-time performance and low network delay. However, there are many problems including privacy disclosure, limited calculation force, as well as scheduling and coordination issues. Federated learning can greatly improves training efficiency. However, due to the sensitive nature of the healthcare data, the aforementioned approach of transferring the patient's data to the servers may create serious security and privacy issues. Therefore, this article proposes a Privacy Protection Scheme for Federated Learning under Edge Computing (PPFLEC). First of all, we propose a lightweight privacy protection protocol based on a shared secret and weight mask, which is based on a random mask scheme of secret sharing. It is more accurate and efficient than,homomorphic encryption. It can not only protect gradient privacy without losing model accuracy, but also resist equipment dropping and collusion attacks between devices. Second, we design an algorithm based on a digital signature and hash function, which achieves the integrity and consistency of the message, as well as resisting replay attacks. Finally, we propose a periodic average training strategy, compared with differential privacy to prove that our scheme is 40 % faster in efficiency than in deferential privacy. Meanwhile, compared with federated learning, we can achieve the same efficiency under the condition of ensuring safety. Therefore, our scheme can work well in unstable edge computing environments such as smart healthcare.