In this paper, we address the problem of image semantic communication in a multi-user deployment scenario and propose a federated learning (FL) strategy for a Swin Transformer-based semantic communication system (FSSC). Firstly, we demonstrate that the adoption of a Swin Transformer for joint source-channel coding (JSCC) effectively extracts semantic information in the communication system. Next, the FL framework is introduced to collaboratively learn a global model by aggregating local model parameters, rather than directly sharing clients' data. This approach enhances user privacy protection and reduces the workload on the server or mobile edge. Simulation evaluations indicate that our method outperforms the typical JSCC algorithm and traditional separate-based communication algorithms. Particularly after integrating local semantics, the global aggregation model has further increased the Peak Signal-to-Noise Ratio (PSNR) by more than 2dB, thoroughly proving the effectiveness of our algorithm.