Semantic communication powered by artificial in-telligence is carried out vigorously to further improve communication efficiency. The knowledge base (KB), as a critical component of semantic communication systems, guides devices to do semantic coding/encoding. However, mismatched KBs hinder semantic alignment between the transceiver and the receiver, which brings severe semantic error. In this work, we design a semantic knowledge base synchronization (SKBS) framework based on federated knowledge distillation for KB establishment and dynamic evolution. In the SKBS, we use the mutual distil-lation mechanism to learn knowledge from heterogeneous local KBs. Meanwhile, the global KB is compressed to improve the synchronization efficiency. Moreover, a filtering method for KB parameters with noise is applied to mitigate the effects of noise for KB synchronization. The experiment results demonstrate that our proposed approach can assist in establishing a universal global KB and improve the accuracy of multi-user semantic communication while reducing the communication cost during KB synchronization.