Unsupervised cross-lingual word embedding(CLWE) methods learn a linear transformation matrix that maps two monolingual embedding spaces that are separately trained with monolingual corpora. This method relies on the assumption that the two embedding spaces are structurally similar, which does not necessarily hold true in general. In this paper, we argue that using a pseudo-parallel corpus generated by an unsupervised machine translation model facilitates the structural similarity of the two embedding spaces and improves the quality of CLWEs in the unsupervised mapping method. We show that our approach outperforms other alternative approaches given the same amount of data, and, through detailed analysis, we show that data augmentation with the pseudo data from unsupervised machine translation is especially effective for mapping-based CLWEs because (1) the pseudo data makes the source and target corpora (partially) parallel; (2) the pseudo data contains information on the original language that helps to learn similar embedding spaces between the source and target languages.