Speaker anonymization is an effective privacy protection solution designed to conceal the speaker's identity while preserving the linguistic content and para-linguistic information of the original speech. While most prior studies focus solely on a single language, an ideal speaker anonymization system should be capable of handling multiple languages. This paper proposes MUSA, a Multi-lingual Speaker Anonymization approach that employs a serial disentanglement strategy to perform a step-by-step disentanglement from a global time-invariant representation to a temporal time-variant representation. By utilizing semantic distillation and self-supervised speaker distillation, the serial disentanglement strategy can avoid strong inductive biases and exhibit superior generalization performance across different languages. Meanwhile, we propose a straightforward anonymization strategy that employs empty embedding with zero values to simulate the speaker identity concealment process, eliminating the need for conversion to a pseudo-speaker identity and thereby reducing the complexity of speaker anonymization process. Experimental results on VoicePrivacy official datasets and multi-lingual datasets demonstrate that MUSA can effectively protect speaker privacy while preserving linguistic content and para-linguistic information.