Multilingual Knowledge Graph Completion (KGC) aims to predict missing links with multilingual knowledge graphs. However, existing approaches suffer from two main drawbacks: (a) alignment dependency: the multilingual KGC is always realized with joint entity or relation alignment, which introduces additional alignment models and increases the complexity of the whole framework; (b) training inefficiency: the trained model will only be used for the completion of one target KG, although the data from all KGs are used simultaneously. To address these drawbacks, we propose a novel multilingual KGC framework with language-sensitive multi-graph attention such that the missing links on all given KGs can be inferred by a universal knowledge completion model. Specifically, we first build a relational graph neural network by sharing the embeddings of aligned nodes to transfer language-independent knowledge. Meanwhile, a language-sensitive multi-graph attention (LSMGA) is proposed to deal with the information inconsistency among different KGs. Experimental results show that our model achieves significant improvements on the DBP-5L and E-PKG datasets.