As an important cyber-physical system (CPS), smart grid is highly vulnerable to cyber attacks. Amongst various types of attacks, false data injection attack (FDIA) proves to be one of the top-priority cyber-related issues and has received increasing attention in recent years. However, so far little attention has been paid to privacy preservation issues in the detection of FDIAs in smart grid. Inspired by federated learning, a FDIA detection method based on secure federated deep learning is proposed in this paper by combining Transformer, federated learning and Paillier cryptosystem. The Transformer, as a detector deployed in edge nodes, delves deep into the connection between individual electrical quantities by using its multi-head self-attention mechanism. By using federated learning framework, our approach utilizes the data from all nodes to collaboratively train a detection model while preserving data privacy by keeping the data locally during training. To improve the security of federated learning, a secure federated learning scheme is designed by combing Paillier cryptosystem with federated learning. Through extensive experiments on the IEEE 14-bus and 118-bus test systems, the effectiveness and superiority of the proposed method are verifed.