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Pre-trained multilingual language models play an important role in cross-lingual natural language understanding tasks. However, existing methods did not focus on learning the semantic structure of representation, and thus could not optimize their performance. In this paper, we propose Multi-level Multilingual Knowledge Distillation (MMKD), a novel method for improving multilingual language models. Specifically, we employ a teacher-student framework to adopt rich semantic representation knowledge in English BERT. We propose token-, word-, sentence-, and structure-level alignment objectives to encourage multiple levels of consistency between source-target pairs and correlation similarity between teacher and student models. We conduct experiments on cross-lingual evaluation benchmarks including XNLI, PAWS-X, and XQuAD. Experimental results show that MMKD outperforms other baseline models of similar size on XNLI and XQuAD and obtains comparable performance on PAWS-X. Especially, MMKD obtains significant performance gains on low-resource languages.